LMFDB - Embedded newform 287.2.h.c.78.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(57,287)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("287.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			78.2
Character	$\chi$	$=$	287.78
Dual form			287.2.h.c.92.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91136 + 1.38868i) q^{2} -1.05524 q^{3} +(1.10682 - 3.40644i) q^{4} +(0.886655 - 2.72884i) q^{5} +(2.01694 - 1.46539i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.15479 + 3.55408i) q^{8} -1.88648 q^{9} +O(q^{10})$	\(q+(-1.91136 + 1.38868i) q^{2} -1.05524 q^{3} +(1.10682 - 3.40644i) q^{4} +(0.886655 - 2.72884i) q^{5} +(2.01694 - 1.46539i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.15479 + 3.55408i) q^{8} -1.88648 q^{9} +(2.09479 + 6.44709i) q^{10} +(0.763287 + 2.34915i) q^{11} +(-1.16796 + 3.59460i) q^{12} +(-3.82457 + 2.77872i) q^{13} +2.36257 q^{14} +(-0.935630 + 2.87957i) q^{15} +(-1.34734 - 0.978898i) q^{16} +(2.33884 + 7.19820i) q^{17} +(3.60574 - 2.61972i) q^{18} +(-5.03769 - 3.66010i) q^{19} +(-8.31428 - 6.04068i) q^{20} +(0.853704 + 0.620252i) q^{21} +(-4.72115 - 3.43012i) q^{22} +(-1.51428 + 1.10019i) q^{23} +(-1.21858 - 3.75039i) q^{24} +(-2.61535 - 1.90016i) q^{25} +(3.45138 - 10.6223i) q^{26} +5.15639 q^{27} +(-2.89769 + 2.10530i) q^{28} +(-2.53256 + 7.79443i) q^{29} +(-2.21049 - 6.80320i) q^{30} +(-1.75753 - 5.40911i) q^{31} -3.53934 q^{32} +(-0.805447 - 2.47891i) q^{33} +(-14.4664 - 10.5104i) q^{34} +(-2.32129 + 1.68652i) q^{35} +(-2.08799 + 6.42617i) q^{36} +(0.185722 - 0.571593i) q^{37} +14.7116 q^{38} +(4.03583 - 2.93220i) q^{39} +10.7224 q^{40} +(5.15150 - 3.80290i) q^{41} -2.49307 q^{42} +(-6.36412 + 4.62380i) q^{43} +8.84708 q^{44} +(-1.67266 + 5.14790i) q^{45} +(1.36652 - 4.20572i) q^{46} +(-3.09804 + 2.25086i) q^{47} +(1.42176 + 1.03297i) q^{48} +(0.309017 + 0.951057i) q^{49} +7.63760 q^{50} +(-2.46802 - 7.59580i) q^{51} +(5.23242 + 16.1037i) q^{52} +(-3.56257 + 10.9645i) q^{53} +(-9.85571 + 7.16059i) q^{54} +7.08725 q^{55} +(1.15479 - 3.55408i) q^{56} +(5.31595 + 3.86227i) q^{57} +(-5.98336 - 18.4149i) q^{58} +(-0.126874 + 0.0921794i) q^{59} +(8.77352 + 6.37434i) q^{60} +(0.358906 + 0.260760i) q^{61} +(10.8708 + 7.89811i) q^{62} +(1.52619 + 1.10884i) q^{63} +(9.45962 - 6.87282i) q^{64} +(4.19160 + 12.9004i) q^{65} +(4.98193 + 3.61958i) q^{66} +(0.807457 - 2.48510i) q^{67} +27.1089 q^{68} +(1.59792 - 1.16096i) q^{69} +(2.09479 - 6.44709i) q^{70} +(-1.71017 - 5.26336i) q^{71} +(-2.17849 - 6.70469i) q^{72} -8.41769 q^{73} +(0.438781 + 1.35043i) q^{74} +(2.75981 + 2.00512i) q^{75} +(-18.0437 + 13.1095i) q^{76} +(0.763287 - 2.34915i) q^{77} +(-3.64202 + 11.2090i) q^{78} -14.4096 q^{79} +(-3.86588 + 2.80873i) q^{80} +0.218230 q^{81} +(-4.56535 + 14.4225i) q^{82} +5.57649 q^{83} +(3.05775 - 2.22158i) q^{84} +21.7165 q^{85} +(5.74312 - 17.6755i) q^{86} +(2.67245 - 8.22496i) q^{87} +(-7.46765 + 5.42557i) q^{88} +(-9.53732 - 6.92927i) q^{89} +(-3.95177 - 12.1623i) q^{90} +4.72743 q^{91} +(2.07169 + 6.37602i) q^{92} +(1.85460 + 5.70789i) q^{93} +(2.79574 - 8.60439i) q^{94} +(-14.4545 + 10.5018i) q^{95} +3.73484 q^{96} +(-0.326183 + 1.00389i) q^{97} +(-1.91136 - 1.38868i) q^{98} +(-1.43992 - 4.43163i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9	\( 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9} + 5 q^{10} - 10 q^{11} - 12 q^{12} - 17 q^{13} + 2 q^{14} - 3 q^{15} - 23 q^{16} - 8 q^{17} - 2 q^{18} + 23 q^{19} - 13 q^{22} - q^{23} + 46 q^{24} - 34 q^{25} + 3 q^{26} - 18 q^{28} - 18 q^{29} - 19 q^{30} - 3 q^{31} - 26 q^{32} - 6 q^{33} - 44 q^{34} + q^{35} - 38 q^{36} - 5 q^{37} + 28 q^{38} + 17 q^{39} + 14 q^{40} - 11 q^{41} - 24 q^{42} + 13 q^{43} + 66 q^{44} + 43 q^{45} - 20 q^{46} - 27 q^{47} + 39 q^{48} - 10 q^{49} + 106 q^{50} - 18 q^{51} - 30 q^{52} - 30 q^{53} - 109 q^{54} + 118 q^{55} + 16 q^{56} - 40 q^{57} - 23 q^{58} - 37 q^{59} + 96 q^{60} - 41 q^{61} - 13 q^{62} - 30 q^{63} + 10 q^{64} + 6 q^{65} - 30 q^{66} - 6 q^{67} - 26 q^{68} - 31 q^{69} + 5 q^{70} - 31 q^{71} + 107 q^{72} - 46 q^{73} + 75 q^{74} - 61 q^{75} + 43 q^{76} - 10 q^{77} + 34 q^{78} + 76 q^{79} + 64 q^{80} + 16 q^{81} - 16 q^{82} - 52 q^{83} - 7 q^{84} + 86 q^{85} - 17 q^{86} - 20 q^{87} - 52 q^{88} - 16 q^{89} + 6 q^{90} + 18 q^{91} + 97 q^{92} + 32 q^{93} - 5 q^{94} - 102 q^{95} + 38 q^{96} - 18 q^{97} - 3 q^{98} - 71 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9 + 5 * q^10 - 10 * q^11 - 12 * q^12 - 17 * q^13 + 2 * q^14 - 3 * q^15 - 23 * q^16 - 8 * q^17 - 2 * q^18 + 23 * q^19 - 13 * q^22 - q^23 + 46 * q^24 - 34 * q^25 + 3 * q^26 - 18 * q^28 - 18 * q^29 - 19 * q^30 - 3 * q^31 - 26 * q^32 - 6 * q^33 - 44 * q^34 + q^35 - 38 * q^36 - 5 * q^37 + 28 * q^38 + 17 * q^39 + 14 * q^40 - 11 * q^41 - 24 * q^42 + 13 * q^43 + 66 * q^44 + 43 * q^45 - 20 * q^46 - 27 * q^47 + 39 * q^48 - 10 * q^49 + 106 * q^50 - 18 * q^51 - 30 * q^52 - 30 * q^53 - 109 * q^54 + 118 * q^55 + 16 * q^56 - 40 * q^57 - 23 * q^58 - 37 * q^59 + 96 * q^60 - 41 * q^61 - 13 * q^62 - 30 * q^63 + 10 * q^64 + 6 * q^65 - 30 * q^66 - 6 * q^67 - 26 * q^68 - 31 * q^69 + 5 * q^70 - 31 * q^71 + 107 * q^72 - 46 * q^73 + 75 * q^74 - 61 * q^75 + 43 * q^76 - 10 * q^77 + 34 * q^78 + 76 * q^79 + 64 * q^80 + 16 * q^81 - 16 * q^82 - 52 * q^83 - 7 * q^84 + 86 * q^85 - 17 * q^86 - 20 * q^87 - 52 * q^88 - 16 * q^89 + 6 * q^90 + 18 * q^91 + 97 * q^92 + 32 * q^93 - 5 * q^94 - 102 * q^95 + 38 * q^96 - 18 * q^97 - 3 * q^98 - 71 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.91136	+	1.38868i	−1.35154	+	0.981948i	−0.352603	+	0.935773i	$0.614703\pi$
$2$	−1.91136	+	1.38868i	−1.35154	+	0.981948i	−0.998933	+	0.0461751i	$0.985297\pi$
$3$	−1.05524			−0.609241			−0.304620	−	0.952474i	$-0.598530\pi$
$3$	−1.05524			−0.609241			−0.304620	+	0.952474i	$0.598530\pi$
$4$	1.10682	−	3.40644i	0.553410	−	1.70322i
$5$	0.886655	−	2.72884i	0.396524	−	1.22038i	−0.531244	−	0.847219i	$-0.678275\pi$
$5$	0.886655	−	2.72884i	0.396524	−	1.22038i	0.927768	−	0.373157i	$-0.121725\pi$
$6$	2.01694	−	1.46539i	0.823411	−	0.598243i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	1.15479	+	3.55408i	0.408280	+	1.25656i
$9$	−1.88648			−0.628826
$10$	2.09479	+	6.44709i	0.662430	+	2.03875i
$11$	0.763287	+	2.34915i	0.230140	+	0.708297i	0.997729	+	0.0673550i	$0.0214560\pi$
$11$	0.763287	+	2.34915i	0.230140	+	0.708297i	−0.767590	+	0.640942i	$0.778544\pi$
$12$	−1.16796	+	3.59460i	−0.337160	+	1.03767i
$13$	−3.82457	+	2.77872i	−1.06075	+	0.770677i	−0.974226	−	0.225573i	$-0.927575\pi$
$13$	−3.82457	+	2.77872i	−1.06075	+	0.770677i	−0.0865196	+	0.996250i	$0.527575\pi$
$14$	2.36257			0.631424
$15$	−0.935630	+	2.87957i	−0.241579	+	0.743503i
$16$	−1.34734	−	0.978898i	−0.336834	−	0.244724i
$17$	2.33884	+	7.19820i	0.567251	+	1.74582i	0.661166	+	0.750240i	$0.270062\pi$
$17$	2.33884	+	7.19820i	0.567251	+	1.74582i	−0.0939148	+	0.995580i	$0.529938\pi$
$18$	3.60574	−	2.61972i	0.849881	−	0.617474i
$19$	−5.03769	−	3.66010i	−1.15573	−	0.839684i	−0.166494	−	0.986042i	$-0.553245\pi$
$19$	−5.03769	−	3.66010i	−1.15573	−	0.839684i	−0.989232	+	0.146358i	$0.953245\pi$
$20$	−8.31428	−	6.04068i	−1.85913	−	1.35074i
$21$	0.853704	+	0.620252i	0.186293	+	0.135350i
$22$	−4.72115	−	3.43012i	−1.00655	−	0.731303i
$23$	−1.51428	+	1.10019i	−0.315749	+	0.229405i	−0.734359	−	0.678761i	$-0.762517\pi$
$23$	−1.51428	+	1.10019i	−0.315749	+	0.229405i	0.418610	+	0.908166i	$0.362517\pi$
$24$	−1.21858	−	3.75039i	−0.248741	−	0.765546i
$25$	−2.61535	−	1.90016i	−0.523069	−	0.380032i
$26$	3.45138	−	10.6223i	0.676871	−	2.08320i
$27$	5.15639			0.992347
$28$	−2.89769	+	2.10530i	−0.547612	+	0.397864i
$29$	−2.53256	+	7.79443i	−0.470285	+	1.44739i	0.381926	+	0.924193i	$0.375261\pi$
$29$	−2.53256	+	7.79443i	−0.470285	+	1.44739i	−0.852212	+	0.523197i	$0.824739\pi$
$30$	−2.21049	−	6.80320i	−0.403579	−	1.24209i
$31$	−1.75753	−	5.40911i	−0.315661	−	0.971505i	−0.975481	−	0.220081i	$-0.929368\pi$
$31$	−1.75753	−	5.40911i	−0.315661	−	0.971505i	0.659820	−	0.751423i	$-0.270632\pi$
$32$	−3.53934			−0.625672
$33$	−0.805447	−	2.47891i	−0.140210	−	0.431523i
$34$	−14.4664	−	10.5104i	−2.48097	−	1.80253i
$35$	−2.32129	+	1.68652i	−0.392370	+	0.285074i
$36$	−2.08799	+	6.42617i	−0.347998	+	1.07103i
$37$	0.185722	−	0.571593i	0.0305325	−	0.0939693i	−0.934629	−	0.355624i	$-0.884268\pi$
$37$	0.185722	−	0.571593i	0.0305325	−	0.0939693i	0.965161	+	0.261655i	$0.0842683\pi$
$38$	14.7116			2.38653
$39$	4.03583	−	2.93220i	0.646249	−	0.469528i
$40$	10.7224			1.69537
$41$	5.15150	−	3.80290i	0.804529	−	0.593913i
$41$	5.15150	−	3.80290i	0.804529	−	0.593913i
$42$	−2.49307			−0.384689
$43$	−6.36412	+	4.62380i	−0.970519	+	0.705123i	−0.955570	−	0.294765i	$-0.904759\pi$
$43$	−6.36412	+	4.62380i	−0.970519	+	0.705123i	−0.0149489	+	0.999888i	$0.504759\pi$
$44$	8.84708			1.33375
$45$	−1.67266	+	5.14790i	−0.249345	+	0.767404i
$46$	1.36652	−	4.20572i	0.201482	−	0.620099i
$47$	−3.09804	+	2.25086i	−0.451895	+	0.328321i	−0.790344	−	0.612664i	$-0.790098\pi$
$47$	−3.09804	+	2.25086i	−0.451895	+	0.328321i	0.338448	+	0.940985i	$0.390098\pi$
$48$	1.42176	+	1.03297i	0.205213	+	0.149096i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	7.63760			1.08012
$51$	−2.46802	−	7.59580i	−0.345593	−	1.06362i
$52$	5.23242	+	16.1037i	0.725605	+	2.23318i
$53$	−3.56257	+	10.9645i	−0.489356	+	1.50608i	0.336215	+	0.941785i	$0.390853\pi$
$53$	−3.56257	+	10.9645i	−0.489356	+	1.50608i	−0.825571	+	0.564298i	$0.809147\pi$
$54$	−9.85571	+	7.16059i	−1.34119	+	0.974433i
$55$	7.08725			0.955644
$56$	1.15479	−	3.55408i	0.154315	−	0.474934i
$57$	5.31595	+	3.86227i	0.704115	+	0.511570i
$58$	−5.98336	−	18.4149i	−0.785654	−	2.41799i
$59$	−0.126874	+	0.0921794i	−0.0165176	+	0.0120007i	−0.596013	−	0.802974i	$-0.703250\pi$
$59$	−0.126874	+	0.0921794i	−0.0165176	+	0.0120007i	0.579496	+	0.814975i	$0.303250\pi$
$60$	8.77352	+	6.37434i	1.13266	+	0.822923i
$61$	0.358906	+	0.260760i	0.0459531	+	0.0333869i	0.610525	−	0.791997i	$-0.290959\pi$
$61$	0.358906	+	0.260760i	0.0459531	+	0.0333869i	−0.564572	+	0.825384i	$0.690959\pi$
$62$	10.8708	+	7.89811i	1.38059	+	1.00306i
$63$	1.52619	+	1.10884i	0.192282	+	0.139701i
$64$	9.45962	−	6.87282i	1.18245	−	0.859102i
$65$	4.19160	+	12.9004i	0.519904	+	1.60010i
$66$	4.98193	+	3.61958i	0.613233	+	0.445540i
$67$	0.807457	−	2.48510i	0.0986466	−	0.303603i	−0.889540	−	0.456857i	$-0.848975\pi$
$67$	0.807457	−	2.48510i	0.0986466	−	0.303603i	0.988187	+	0.153254i	$0.0489752\pi$
$68$	27.1089			3.28744
$69$	1.59792	−	1.16096i	0.192367	−	0.139763i
$70$	2.09479	−	6.44709i	0.250375	−	0.770575i
$71$	−1.71017	−	5.26336i	−0.202960	−	0.624646i	−0.999791	−	0.0204442i	$-0.993492\pi$
$71$	−1.71017	−	5.26336i	−0.202960	−	0.624646i	0.796831	−	0.604202i	$-0.206508\pi$
$72$	−2.17849	−	6.70469i	−0.256737	−	0.790156i
$73$	−8.41769			−0.985216			−0.492608	−	0.870251i	$-0.663956\pi$
$73$	−8.41769			−0.985216			−0.492608	+	0.870251i	$0.663956\pi$
$74$	0.438781	+	1.35043i	0.0510073	+	0.156984i
$75$	2.75981	+	2.00512i	0.318675	+	0.231531i
$76$	−18.0437	+	13.1095i	−2.06976	+	1.50377i
$77$	0.763287	−	2.34915i	0.0869846	−	0.267711i
$78$	−3.64202	+	11.2090i	−0.412377	+	1.26917i
$79$	−14.4096			−1.62120			−0.810601	−	0.585599i	$-0.800859\pi$
$79$	−14.4096			−1.62120			−0.810601	+	0.585599i	$0.800859\pi$
$80$	−3.86588	+	2.80873i	−0.432219	+	0.314025i
$81$	0.218230			0.0242478
$82$	−4.56535	+	14.4225i	−0.504158	+	1.59270i
$83$	5.57649			0.612100			0.306050	−	0.952016i	$-0.400993\pi$
$83$	5.57649			0.612100			0.306050	+	0.952016i	$0.400993\pi$
$84$	3.05775	−	2.22158i	0.333628	−	0.242395i
$85$	21.7165			2.35549
$86$	5.74312	−	17.6755i	0.619296	−	1.90600i
$87$	2.67245	−	8.22496i	0.286517	−	0.881809i
$88$	−7.46765	+	5.42557i	−0.796054	+	0.578367i
$89$	−9.53732	−	6.92927i	−1.01095	−	0.734501i	−0.0465452	−	0.998916i	$-0.514821\pi$
$89$	−9.53732	−	6.92927i	−1.01095	−	0.734501i	−0.964409	+	0.264415i	$0.914821\pi$
$90$	−3.95177	−	12.1623i	−0.416553	−	1.28202i
$91$	4.72743			0.495570
$92$	2.07169	+	6.37602i	0.215989	+	0.664746i
$93$	1.85460	+	5.70789i	0.192314	+	0.591880i
$94$	2.79574	−	8.60439i	0.288358	−	0.887475i
$95$	−14.4545	+	10.5018i	−1.48300	+	1.07747i
$96$	3.73484			0.381185
$97$	−0.326183	+	1.00389i	−0.0331188	+	0.101929i	−0.966249	−	0.257608i	$-0.917066\pi$
$97$	−0.326183	+	1.00389i	−0.0331188	+	0.101929i	0.933131	+	0.359538i	$0.117066\pi$
$98$	−1.91136	−	1.38868i	−0.193077	−	0.140278i
$99$	−1.43992	−	4.43163i	−0.144718	−	0.445395i
$100$	−9.36750	+	6.80589i	−0.936750	+	0.680589i
$101$	8.95912	+	6.50918i	0.891466	+	0.647688i	0.936260	−	0.351308i	$-0.114263\pi$
$101$	8.95912	+	6.50918i	0.891466	+	0.647688i	−0.0447938	+	0.998996i	$0.514263\pi$
$102$	15.2655	+	11.0910i	1.51150	+	1.09817i
$103$	5.97687	+	4.34245i	0.588918	+	0.427874i	0.841928	−	0.539589i	$-0.181421\pi$
$103$	5.97687	+	4.34245i	0.588918	+	0.427874i	−0.253010	+	0.967464i	$0.581421\pi$
$104$	−14.2924	−	10.3840i	−1.40148	−	1.01824i
$105$	2.44951	−	1.77967i	0.239048	−	0.173678i
$106$	−8.41682	−	25.9043i	−0.817514	−	2.51605i
$107$	−9.17543	−	6.66634i	−0.887023	−	0.644460i	0.0480774	−	0.998844i	$-0.484691\pi$
$107$	−9.17543	−	6.66634i	−0.887023	−	0.644460i	−0.935100	+	0.354384i	$0.884691\pi$
$108$	5.70719	−	17.5649i	0.549175	−	1.69019i
$109$	8.05945			0.771955			0.385978	−	0.922508i	$-0.373864\pi$
$109$	8.05945			0.771955			0.385978	+	0.922508i	$0.373864\pi$
$110$	−13.5463	+	9.84195i	−1.29159	+	0.938393i
$111$	−0.195980	+	0.603165i	−0.0186016	+	0.0572499i
$112$	0.514637	+	1.58389i	0.0486286	+	0.149664i
$113$	−4.40978	−	13.5719i	−0.414837	−	1.27674i	−0.912396	−	0.409308i	$-0.865770\pi$
$113$	−4.40978	−	13.5719i	−0.414837	−	1.27674i	0.497559	−	0.867430i	$-0.334230\pi$
$114$	−15.5242			−1.45397
$115$	1.65960	+	5.10772i	0.154758	+	0.476298i
$116$	23.7482	+	17.2541i	2.20496	+	1.60200i
$117$	7.21497	−	5.24198i	0.667024	−	0.484622i
$118$	0.114494	−	0.352376i	0.0105400	−	0.0324388i
$119$	2.33884	−	7.19820i	0.214401	−	0.659858i
$120$	−11.3147			−1.03289
$121$	3.96327	−	2.87948i	0.360297	−	0.261771i
$122$	−1.04811			−0.0948915
$123$	−5.43605	+	4.01296i	−0.490152	+	0.361836i
$124$	−20.3711			−1.82938
$125$	4.10231	−	2.98050i	0.366922	−	0.266584i
$126$	−4.45694			−0.397056
$127$	−2.70736	+	8.33240i	−0.240240	+	0.739381i	0.756143	+	0.654406i	$0.227081\pi$
$127$	−2.70736	+	8.33240i	−0.240240	+	0.739381i	−0.996383	+	0.0849755i	$0.972919\pi$
$128$	−6.34914	+	19.5406i	−0.561190	+	1.72717i
$129$	6.71564	−	4.87920i	0.591279	−	0.429590i
$130$	−25.9263	−	18.8366i	−2.27389	−	1.65207i
$131$	−2.57631	−	7.92908i	−0.225094	−	0.692767i	−0.998282	−	0.0585905i	$-0.981339\pi$
$131$	−2.57631	−	7.92908i	−0.225094	−	0.692767i	0.773189	−	0.634176i	$-0.218661\pi$
$132$	−9.33575			−0.812573
$133$	1.92423	+	5.92216i	0.166852	+	0.513517i
$134$	1.90767	+	5.87122i	0.164798	+	0.507196i
$135$	4.57194	−	14.0710i	0.393490	−	1.21104i
$136$	−22.8821	+	16.6248i	−1.96213	+	1.42557i
$137$	−7.96601			−0.680583			−0.340291	−	0.940320i	$-0.610526\pi$
$137$	−7.96601			−0.680583			−0.340291	+	0.940320i	$0.610526\pi$
$138$	−1.44200	+	4.43802i	−0.122751	+	0.377789i
$139$	−1.99260	−	1.44771i	−0.169010	−	0.122793i	0.500065	−	0.865988i	$-0.333310\pi$
$139$	−1.99260	−	1.44771i	−0.169010	−	0.122793i	−0.669075	+	0.743195i	$0.733310\pi$
$140$	3.17577	+	9.77402i	0.268402	+	0.826055i
$141$	3.26916	−	2.37518i	0.275313	−	0.200027i
$142$	10.5779	+	7.68530i	0.887678	+	0.644936i
$143$	−9.44688	−	6.86356i	−0.789988	−	0.573960i
$144$	2.54172	+	1.84667i	0.211810	+	0.153889i
$145$	19.0243	+	13.8219i	1.57988	+	1.14785i
$146$	16.0892	−	11.6895i	1.33155	−	0.967431i
$147$	−0.326086	−	1.00359i	−0.0268951	−	0.0827746i
$148$	−1.74154	−	1.26530i	−0.143153	−	0.104007i
$149$	−3.51793	+	10.8271i	−0.288200	+	0.886989i	0.697221	+	0.716856i	$0.254420\pi$
$149$	−3.51793	+	10.8271i	−0.288200	+	0.886989i	−0.985421	+	0.170133i	$0.945580\pi$
$150$	−8.05946			−0.658052
$151$	−16.9331	+	12.3026i	−1.37799	+	1.00117i	−0.380929	+	0.924604i	$0.624396\pi$
$151$	−16.9331	+	12.3026i	−1.37799	+	1.00117i	−0.997064	+	0.0765667i	$0.975604\pi$
$152$	7.19080	−	22.1310i	0.583251	−	1.79506i
$153$	−4.41216	−	13.5792i	−0.356702	−	1.09782i
$154$	1.80332	+	5.55005i	0.145316	+	0.447235i
$155$	−16.3189			−1.31077
$156$	−5.52143	−	16.9932i	−0.442068	−	1.36055i
$157$	−4.86161	−	3.53217i	−0.387999	−	0.281898i	0.376636	−	0.926361i	$-0.377081\pi$
$157$	−4.86161	−	3.53217i	−0.387999	−	0.281898i	−0.764635	+	0.644464i	$0.777081\pi$
$158$	27.5419	−	20.0103i	2.19111	−	1.59194i
$159$	3.75935	−	11.5701i	0.298136	−	0.917567i
$160$	−3.13817	+	9.65830i	−0.248094	+	0.763556i
$161$	1.87175			0.147515
$162$	−0.417116	+	0.303053i	−0.0327717	+	0.0238101i
$163$	−2.85713			−0.223787			−0.111894	−	0.993720i	$-0.535692\pi$
$163$	−2.85713			−0.223787			−0.111894	+	0.993720i	$0.535692\pi$
$164$	−7.25257	−	21.7574i	−0.566330	−	1.69897i
$165$	−7.47872			−0.582217
$166$	−10.6587	+	7.74399i	−0.827274	+	0.601050i
$167$	8.87817			0.687013			0.343507	−	0.939150i	$-0.388385\pi$
$167$	8.87817			0.687013			0.343507	+	0.939150i	$0.388385\pi$
$168$	−1.21858	+	3.75039i	−0.0940152	+	0.289349i
$169$	2.88888	−	8.89107i	0.222222	−	0.683928i
$170$	−41.5081	+	30.1574i	−3.18352	+	2.31297i
$171$	9.50349	+	6.90469i	0.726750	+	0.528015i
$172$	8.70678	+	26.7967i	0.663885	+	2.04323i
$173$	2.02254			0.153771			0.0768853	−	0.997040i	$-0.475502\pi$
$173$	2.02254			0.153771			0.0768853	+	0.997040i	$0.475502\pi$
$174$	6.31386	+	19.4321i	0.478652	+	1.47314i
$175$	0.998974	+	3.07453i	0.0755153	+	0.232412i
$176$	1.27118	−	3.91228i	0.0958186	−	0.294899i
$177$	0.133882	−	0.0972710i	0.0100632	−	0.00731133i
$178$	27.8518			2.08758
$179$	2.61688	−	8.05391i	0.195594	−	0.601978i	−0.804375	−	0.594122i	$-0.797499\pi$
$179$	2.61688	−	8.05391i	0.195594	−	0.601978i	0.999969	−	0.00785547i	$-0.00250050\pi$
$180$	15.6847	+	11.3956i	1.16907	+	0.849378i
$181$	5.87248	+	18.0736i	0.436498	+	1.34340i	0.891544	+	0.452935i	$0.149623\pi$
$181$	5.87248	+	18.0736i	0.436498	+	1.34340i	−0.455045	+	0.890468i	$0.650377\pi$
$182$	−9.03583	+	6.56491i	−0.669780	+	0.486624i
$183$	−0.378730	−	0.275163i	−0.0279965	−	0.0203407i
$184$	−5.65884	−	4.11139i	−0.417175	−	0.303095i
$185$	−1.39512	−	1.01361i	−0.102571	−	0.0745222i
$186$	−11.4713	−	8.33437i	−0.841114	−	0.611105i
$187$	−15.1245	+	10.9886i	−1.10601	+	0.803564i
$188$	4.23844	+	13.0446i	0.309120	+	0.951373i
$189$	−4.17160	−	3.03085i	−0.303440	−	0.220462i
$190$	13.0441	−	40.1456i	0.946318	−	2.91247i
$191$	14.0535			1.01688			0.508438	−	0.861099i	$-0.330223\pi$
$191$	14.0535			1.01688			0.508438	+	0.861099i	$0.330223\pi$
$192$	−9.98213	+	7.25244i	−0.720398	+	0.523400i
$193$	4.63983	−	14.2799i	0.333982	−	1.02789i	−0.633239	−	0.773956i	$-0.718275\pi$
$193$	4.63983	−	14.2799i	0.333982	−	1.02789i	0.967221	−	0.253935i	$-0.0817248\pi$
$194$	−0.770629	−	2.37175i	−0.0553280	−	0.170282i
$195$	−4.42313	−	13.6130i	−0.316747	−	0.974847i
$196$	3.58174			0.255839
$197$	4.79756	+	14.7654i	0.341812	+	1.05199i	0.963268	+	0.268541i	$0.0865413\pi$
$197$	4.79756	+	14.7654i	0.341812	+	1.05199i	−0.621456	+	0.783449i	$0.713459\pi$
$198$	8.90634	+	6.47084i	0.632946	+	0.459862i
$199$	18.2959	−	13.2928i	1.29697	−	0.942300i	0.297044	−	0.954864i	$-0.403999\pi$
$199$	18.2959	−	13.2928i	1.29697	−	0.942300i	0.999921	+	0.0125636i	$0.00399922\pi$
$200$	3.73315	−	11.4894i	0.263973	−	0.812427i
$201$	−0.852057	+	2.62236i	−0.0600995	+	0.184967i
$202$	−26.1633			−1.84084
$203$	6.63034	−	4.81722i	0.465359	−	0.338103i
$204$	−28.6063			−2.00284
$205$	−5.80991	−	17.4295i	−0.405782	−	1.21733i
$206$	−17.4542			−1.21609
$207$	2.85666	−	2.07548i	0.198551	−	0.144256i
$208$	7.87307			0.545899
$209$	4.75293	−	14.6280i	0.328767	−	1.01184i
$210$	−2.21049	+	6.80320i	−0.152539	+	0.469465i
$211$	−5.91383	+	4.29665i	−0.407125	+	0.295793i	−0.772437	−	0.635092i	$-0.780962\pi$
$211$	−5.91383	+	4.29665i	−0.407125	+	0.295793i	0.365312	+	0.930885i	$0.380962\pi$
$212$	33.4066	+	24.2713i	2.29438	+	1.66696i
$213$	1.80463	+	5.55409i	0.123651	+	0.380560i
$214$	26.7950			1.83167
$215$	6.97486	+	21.4664i	0.475681	+	1.46400i
$216$	5.95455	+	18.3262i	0.405156	+	1.24694i
$217$	−1.75753	+	5.40911i	−0.119309	+	0.367194i
$218$	−15.4045	+	11.1920i	−1.04333	+	0.758020i
$219$	8.88265			0.600234
$220$	7.84431	−	24.1423i	0.528863	−	1.62767i
$221$	−28.9468	−	21.0311i	−1.94717	−	1.41470i
$222$	−0.463017	−	1.42502i	−0.0310757	−	0.0956412i
$223$	4.81217	−	3.49625i	0.322247	−	0.234126i	−0.414887	−	0.909873i	$-0.636179\pi$
$223$	4.81217	−	3.49625i	0.322247	−	0.234126i	0.737134	+	0.675747i	$0.236179\pi$
$224$	2.86338	+	2.08037i	0.191318	+	0.139001i
$225$	4.93379	+	3.58461i	0.328920	+	0.238974i
$226$	27.2758	+	19.8170i	1.81436	+	1.31821i
$227$	−0.616223	−	0.447712i	−0.0409001	−	0.0297157i	0.567147	−	0.823616i	$-0.308047\pi$
$227$	−0.616223	−	0.447712i	−0.0409001	−	0.0297157i	−0.608048	+	0.793901i	$0.708047\pi$
$228$	19.0404	−	13.8336i	1.26098	−	0.916156i
$229$	−2.47622	−	7.62103i	−0.163633	−	0.503612i	0.835299	−	0.549795i	$-0.185294\pi$
$229$	−2.47622	−	7.62103i	−0.163633	−	0.503612i	−0.998933	+	0.0461831i	$0.985294\pi$
$230$	−10.2651	−	7.45804i	−0.676861	−	0.491768i
$231$	−0.805447	+	2.47891i	−0.0529945	+	0.163100i
$232$	−30.6266			−2.01074
$233$	7.66386	−	5.56812i	0.502076	−	0.364779i	−0.307733	−	0.951473i	$-0.599571\pi$
$233$	7.66386	−	5.56812i	0.502076	−	0.364779i	0.809809	+	0.586693i	$0.199571\pi$
$234$	−6.51095	+	20.0386i	−0.425634	+	1.30997i
$235$	3.39534	+	10.4498i	0.221488	+	0.681669i
$236$	0.173577	+	0.534215i	0.0112989	+	0.0347744i
$237$	15.2055			0.987702
$238$	5.52567	+	17.0063i	0.358176	+	1.10235i
$239$	1.26954	+	0.922373i	0.0821196	+	0.0596634i	0.628088	−	0.778143i	$-0.283838\pi$
$239$	1.26954	+	0.922373i	0.0821196	+	0.0596634i	−0.545968	+	0.837806i	$0.683838\pi$
$240$	4.07942	−	2.96387i	0.263325	−	0.191317i
$241$	3.88068	−	11.9435i	0.249976	−	0.769348i	−0.744802	−	0.667286i	$-0.767456\pi$
$241$	3.88068	−	11.9435i	0.249976	−	0.769348i	0.994778	−	0.102062i	$-0.0325441\pi$
$242$	−3.57654	+	11.0075i	−0.229909	+	0.707586i
$243$	−15.6994			−1.00712
$244$	1.28551	−	0.933976i	0.0822962	−	0.0597917i
$245$	2.86928			0.183311
$246$	4.81752	−	15.2192i	0.307154	−	0.970338i
$247$	29.4374			1.87306
$248$	17.1948	−	12.4928i	1.09187	−	0.793292i
$249$	−5.88451			−0.372916
$250$	−3.70202	+	11.3936i	−0.234136	+	0.720597i
$251$	−4.61427	+	14.2013i	−0.291250	+	0.896376i	0.693205	+	0.720741i	$0.256198\pi$
$251$	−4.61427	+	14.2013i	−0.291250	+	0.896376i	−0.984455	+	0.175636i	$0.943802\pi$
$252$	5.46643	−	3.97159i	0.344353	−	0.250187i
$253$	−3.74034	−	2.71752i	−0.235153	−	0.170849i
$254$	−6.39634	−	19.6859i	−0.401342	−	1.23520i
$255$	−22.9160			−1.43506
$256$	−7.77379	−	23.9253i	−0.485862	−	1.49533i
$257$	1.70856	+	5.25841i	0.106577	+	0.328011i	0.990097	−	0.140382i	$-0.0448332\pi$
$257$	1.70856	+	5.25841i	0.106577	+	0.328011i	−0.883520	+	0.468393i	$0.844833\pi$
$258$	−6.06034	+	18.6518i	−0.377301	+	1.16121i
$259$	−0.486226	+	0.353264i	−0.0302126	+	0.0219508i
$260$	48.5839			3.01304
$261$	4.77763	−	14.7040i	0.295728	−	0.910156i
$262$	15.9353	+	11.5776i	0.984483	+	0.715269i
$263$	−5.09707	−	15.6872i	−0.314299	−	0.967311i	−0.976042	−	0.217581i	$-0.930183\pi$
$263$	−5.09707	−	15.6872i	−0.314299	−	0.967311i	0.661744	−	0.749730i	$-0.269817\pi$
$264$	7.88013	−	5.72525i	0.484989	−	0.352365i
$265$	26.7615	+	19.4434i	1.64395	+	1.19440i
$266$	−11.9019	−	8.64724i	−0.729753	−	0.530196i
$267$	10.0641	+	7.31201i	0.615914	+	0.447488i
$268$	−7.57162	−	5.50111i	−0.462511	−	0.336034i
$269$	−19.9570	+	14.4996i	−1.21680	+	0.884055i	−0.995830	−	0.0912266i	$-0.970921\pi$
$269$	−19.9570	+	14.4996i	−1.21680	+	0.884055i	−0.220967	+	0.975281i	$0.570921\pi$
$270$	10.8015	+	33.2437i	0.657360	+	2.02315i
$271$	13.8938	+	10.0944i	0.843986	+	0.613192i	0.923481	−	0.383644i	$-0.125331\pi$
$271$	13.8938	+	10.0944i	0.843986	+	0.613192i	−0.0794953	+	0.996835i	$0.525331\pi$
$272$	3.89510	−	11.9879i	0.236175	−	0.726872i
$273$	−4.98856			−0.301921
$274$	15.2259	−	11.0623i	0.919832	−	0.668297i
$275$	2.46751	−	7.59422i	0.148797	−	0.457949i
$276$	−2.18612	−	6.72820i	−0.131589	−	0.404990i
$277$	−5.56414	−	17.1246i	−0.334317	−	1.02892i	−0.967058	−	0.254557i	$-0.918070\pi$
$277$	−5.56414	−	17.1246i	−0.334317	−	1.02892i	0.632741	−	0.774363i	$-0.281930\pi$
$278$	5.81899			0.349000
$279$	3.31553	+	10.2042i	0.198496	+	0.610907i
$280$	−8.67463	−	6.30249i	−0.518408	−	0.376646i
$281$	−20.7658	+	15.0872i	−1.23878	+	0.900027i	−0.997517	−	0.0704319i	$-0.977562\pi$
$281$	−20.7658	+	15.0872i	−1.23878	+	0.900027i	−0.241265	+	0.970459i	$0.577562\pi$
$282$	−2.95016	+	9.07966i	−0.175680	+	0.540686i
$283$	−0.963834	+	2.96638i	−0.0572940	+	0.176333i	−0.975608	−	0.219520i	$-0.929551\pi$
$283$	−0.963834	+	2.96638i	−0.0572940	+	0.176333i	0.918314	+	0.395853i	$0.129551\pi$
$284$	−19.8222			−1.17623
$285$	15.2529	−	11.0819i	0.903506	−	0.656436i
$286$	27.5877			1.63130
$287$	−6.40294	+	0.0486342i	−0.377954	+	0.00287078i
$288$	6.67688			0.393439
$289$	−32.5906	+	23.6785i	−1.91710	+	1.39285i
$290$	−55.5566			−3.26239
$291$	0.344199	−	1.05934i	0.0201773	−	0.0620994i
$292$	−9.31686	+	28.6744i	−0.545228	+	1.67804i
$293$	−14.4387	+	10.4903i	−0.843519	+	0.612853i	−0.923352	−	0.383956i	$-0.874562\pi$
$293$	−14.4387	+	10.4903i	−0.843519	+	0.612853i	0.0798322	+	0.996808i	$0.474562\pi$
$294$	2.01694	+	1.46539i	0.117630	+	0.0854633i
$295$	0.139050	+	0.427951i	0.00809578	+	0.0249163i
$296$	2.24596			0.130544
$297$	3.93580	+	12.1131i	0.228378	+	0.702876i
$298$	−8.31137	−	25.5798i	−0.481465	−	1.48180i
$299$	2.73436	−	8.41551i	0.158132	−	0.486681i
$300$	9.88492	−	7.18182i	0.570706	−	0.414642i
$301$	7.86648			0.453416
$302$	15.2808	−	47.0294i	0.879310	−	2.70624i
$303$	−9.45399	−	6.86872i	−0.543117	−	0.394598i
$304$	3.20461	+	9.86277i	0.183797	+	0.565669i
$305$	1.02980	−	0.748193i	0.0589661	−	0.0428414i
$306$	27.2905	+	19.8277i	1.56010	+	1.13348i
$307$	−15.0147	−	10.9088i	−0.856936	−	0.622600i	0.0701137	−	0.997539i	$-0.477664\pi$
$307$	−15.0147	−	10.9088i	−0.856936	−	0.622600i	−0.927050	+	0.374939i	$0.877664\pi$
$308$	−7.15743	−	5.20018i	−0.407833	−	0.296308i
$309$	−6.30701	−	4.58231i	−0.358793	−	0.260678i
$310$	31.1914	−	22.6619i	1.77155	−	1.28711i
$311$	−2.26429	−	6.96878i	−0.128396	−	0.395163i	0.866108	−	0.499856i	$-0.166614\pi$
$311$	−2.26429	−	6.96878i	−0.128396	−	0.395163i	−0.994505	+	0.104693i	$0.966614\pi$
$312$	15.0818	+	10.9576i	0.853839	+	0.620351i
$313$	7.83910	−	24.1263i	0.443092	−	1.36370i	−0.441470	−	0.897276i	$-0.645543\pi$
$313$	7.83910	−	24.1263i	0.443092	−	1.36370i	0.884563	−	0.466422i	$-0.154457\pi$
$314$	14.1974			0.801203
$315$	4.37907	−	3.18158i	0.246733	−	0.179262i
$316$	−15.9488	+	49.0853i	−0.897189	+	2.76126i
$317$	3.18948	+	9.81620i	0.179139	+	0.551333i	0.999798	−	0.0200848i	$-0.00639362\pi$
$317$	3.18948	+	9.81620i	0.179139	+	0.551333i	−0.820659	+	0.571418i	$0.806394\pi$
$318$	8.88173	+	27.3351i	0.498062	+	1.53288i
$319$	−20.2434			−1.13341
$320$	−10.3674	−	31.9077i	−0.579557	−	1.78369i
$321$	9.68224	+	7.03456i	0.540410	+	0.392631i
$322$	−3.57760	+	2.59927i	−0.199372	+	0.144852i
$323$	14.5638	−	44.8227i	0.810350	−	2.49400i
$324$	0.241541	−	0.743388i	0.0134190	−	0.0412993i
$325$	15.2826			0.847726
$326$	5.46100	−	3.96765i	0.302457	−	0.219748i
$327$	−8.50462			−0.470306
$328$	19.4647	+	13.9173i	1.07476	+	0.768454i
$329$	3.82938			0.211121
$330$	14.2945	−	10.3856i	0.786888	−	0.571707i
$331$	−32.9790			−1.81269			−0.906346	−	0.422536i	$-0.861140\pi$
$331$	−32.9790			−1.81269			−0.906346	+	0.422536i	$0.861140\pi$
$332$	6.17217	−	18.9960i	0.338742	−	1.04254i
$333$	−0.350360	+	1.07830i	−0.0191996	+	0.0590903i
$334$	−16.9694	+	12.3290i	−0.928523	+	0.674612i
$335$	−6.06551	−	4.40685i	−0.331394	−	0.240772i
$336$	−0.543063	−	1.67138i	−0.0296265	−	0.0911811i
$337$	−2.82559			−0.153919			−0.0769597	−	0.997034i	$-0.524521\pi$
$337$	−2.82559			−0.153919			−0.0769597	+	0.997034i	$0.524521\pi$
$338$	6.82519	+	21.0058i	0.371241	+	1.14256i
$339$	4.65336	+	14.3216i	0.252736	+	0.777841i
$340$	24.0363	−	73.9760i	1.30355	−	4.01191i
$341$	11.3653	−	8.25740i	0.615468	−	0.447163i
$342$	−27.7530			−1.50071
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	−23.7826	−	17.2791i	−1.28227	−	0.931625i
$345$	−1.75127	−	5.38985i	−0.0942851	−	0.290180i
$346$	−3.86579	+	2.80866i	−0.207826	+	0.150995i
$347$	−4.04925	−	2.94195i	−0.217375	−	0.157932i	0.473769	−	0.880649i	$-0.342893\pi$
$347$	−4.04925	−	2.94195i	−0.217375	−	0.157932i	−0.691144	+	0.722717i	$0.742893\pi$
$348$	−25.0599	−	18.2071i	−1.34335	−	0.976003i
$349$	−2.67931	−	1.94663i	−0.143420	−	0.104201i	0.513762	−	0.857933i	$-0.328252\pi$
$349$	−2.67931	−	1.94663i	−0.143420	−	0.104201i	−0.657182	+	0.753732i	$0.728252\pi$
$350$	−6.17894	−	4.48927i	−0.330278	−	0.239961i
$351$	−19.7210	+	14.3281i	−1.05263	+	0.764779i
$352$	−2.70153	−	8.31445i	−0.143992	−	0.443162i
$353$	−3.81381	−	2.77089i	−0.202988	−	0.147480i	0.481647	−	0.876365i	$-0.340039\pi$
$353$	−3.81381	−	2.77089i	−0.202988	−	0.147480i	−0.684636	+	0.728885i	$0.740039\pi$
$354$	−0.120818	+	0.371840i	−0.00642141	+	0.0197631i
$355$	−15.8792			−0.842782
$356$	−34.1602	+	24.8189i	−1.81049	+	1.31540i
$357$	−2.46802	+	7.59580i	−0.130622	+	0.402012i
$358$	6.18255	+	19.0279i	0.326758	+	1.00566i
$359$	7.68934	+	23.6653i	0.405828	+	1.24901i	0.920202	+	0.391443i	$0.128024\pi$
$359$	7.68934	+	23.6653i	0.405828	+	1.24901i	−0.514374	+	0.857566i	$0.671976\pi$
$360$	−20.2276			−1.06609
$361$	6.11071	+	18.8068i	0.321616	+	0.989833i
$362$	−36.3230	−	26.3902i	−1.90910	−	1.38704i
$363$	−4.18218	+	3.03853i	−0.219508	+	0.159482i
$364$	5.23242	−	16.1037i	0.274253	−	0.844064i
$365$	−7.46359	+	22.9706i	−0.390662	+	1.20233i
$366$	1.10600			0.0578118
$367$	7.72205	−	5.61040i	0.403088	−	0.292860i	−0.367710	−	0.929941i	$-0.619858\pi$
$367$	7.72205	−	5.61040i	0.403088	−	0.292860i	0.770798	+	0.637080i	$0.219858\pi$
$368$	3.11722			0.162496
$369$	−9.71819	+	7.17408i	−0.505909	+	0.373468i
$370$	4.07416			0.211805
$371$	9.32692	−	6.77640i	0.484230	−	0.351813i
$372$	21.4963			1.11453
$373$	−10.8746	+	33.4686i	−0.563066	+	1.73294i	0.110562	+	0.993869i	$0.464735\pi$
$373$	−10.8746	+	33.4686i	−0.563066	+	1.73294i	−0.673628	+	0.739071i	$0.735265\pi$
$374$	13.6487	−	42.0063i	0.705756	−	2.17209i
$375$	−4.32891	+	3.14513i	−0.223544	+	0.162414i
$376$	−11.5773	−	8.41141i	−0.597054	−	0.433785i
$377$	−11.9725	−	36.8477i	−0.616617	−	1.89775i
$378$	12.1823			0.626591
$379$	−7.42869	−	22.8632i	−0.381586	−	1.17440i	−0.938927	−	0.344117i	$-0.888178\pi$
$379$	−7.42869	−	22.8632i	−0.381586	−	1.17440i	0.557340	−	0.830284i	$-0.311822\pi$
$380$	19.7753	+	60.8621i	1.01445	+	3.12216i
$381$	2.85691	−	8.79265i	0.146364	−	0.450461i
$382$	−26.8613	+	19.5159i	−1.37434	+	0.998520i
$383$	−32.2429			−1.64753			−0.823767	−	0.566929i	$-0.808132\pi$
$383$	−32.2429			−1.64753			−0.823767	+	0.566929i	$0.808132\pi$
$384$	6.69984	−	20.6200i	0.341900	−	1.05226i
$385$	−5.73370	−	4.16578i	−0.292217	−	0.212308i
$386$	10.9619	+	33.7373i	0.557947	+	1.71718i
$387$	12.0058	−	8.72270i	0.610287	−	0.443400i
$388$	3.05865	+	2.22224i	0.155280	+	0.112817i
$389$	12.8771	+	9.35579i	0.652897	+	0.474357i	0.864257	−	0.503051i	$-0.167789\pi$
$389$	12.8771	+	9.35579i	0.652897	+	0.474357i	−0.211360	+	0.977408i	$0.567789\pi$
$390$	27.3583	+	19.8770i	1.38534	+	1.00651i
$391$	−11.4610	−	8.32693i	−0.579609	−	0.421111i
$392$	−3.02328	+	2.19654i	−0.152699	+	0.110942i
$393$	2.71862	+	8.36705i	0.137136	+	0.422062i
$394$	−29.6743	−	21.5597i	−1.49497	−	1.08616i
$395$	−12.7763	+	39.3214i	−0.642846	+	1.97848i
$396$	−16.6898			−0.838694
$397$	−3.03588	+	2.20569i	−0.152366	+	0.110701i	−0.661357	−	0.750072i	$-0.730019\pi$
$397$	−3.03588	+	2.20569i	−0.152366	+	0.110701i	0.508990	+	0.860772i	$0.330019\pi$
$398$	−16.5107	+	50.8146i	−0.827605	+	2.54711i
$399$	−2.03051	−	6.24928i	−0.101653	−	0.312855i
$400$	1.66369	+	5.12031i	0.0831846	+	0.256016i
$401$	18.6216			0.929920			0.464960	−	0.885332i	$-0.346069\pi$
$401$	18.6216			0.929920			0.464960	+	0.885332i	$0.346069\pi$
$402$	−2.01305	−	6.19552i	−0.100402	−	0.309004i
$403$	21.7522	+	15.8039i	1.08355	+	0.787247i
$404$	32.0893	−	23.3142i	1.59650	−	1.15993i
$405$	0.193495	−	0.595516i	0.00961483	−	0.0295914i
$406$	−5.98336	+	18.4149i	−0.296949	+	0.913916i
$407$	1.48452			0.0735849
$408$	24.1460	−	17.5431i	1.19541	−	0.868514i
$409$	17.4968			0.865159			0.432579	−	0.901596i	$-0.357603\pi$
$409$	17.4968			0.865159			0.432579	+	0.901596i	$0.357603\pi$
$410$	35.3089	+	25.2459i	1.74378	+	1.24681i
$411$	8.40602			0.414639
$412$	21.4076	−	15.5535i	1.05468	−	0.766268i
$413$	0.156825			0.00771685
$414$	−2.57791	+	7.93399i	−0.126697	+	0.389934i
$415$	4.94443	−	15.2174i	0.242712	−	0.746992i
$416$	13.5365	−	9.83481i	0.663679	−	0.482191i
$417$	2.10266	+	1.52767i	0.102968	+	0.0748105i
$418$	11.2291	+	34.5597i	0.549235	+	1.69037i
$419$	−17.5169			−0.855757			−0.427879	−	0.903836i	$-0.640739\pi$
$419$	−17.5169			−0.855757			−0.427879	+	0.903836i	$0.640739\pi$
$420$	−3.35119	−	10.3139i	−0.163521	−	0.503267i
$421$	2.71915	+	8.36867i	0.132523	+	0.407864i	0.995197	−	0.0978972i	$-0.0312116\pi$
$421$	2.71915	+	8.36867i	0.132523	+	0.407864i	−0.862673	+	0.505761i	$0.831212\pi$
$422$	5.33677	−	16.4249i	0.259790	−	0.799551i
$423$	5.84438	−	4.24619i	0.284163	−	0.206457i
$424$	−43.0826			−2.09227
$425$	7.56087	−	23.2700i	0.366756	−	1.12876i
$426$	−11.1622	−	8.10980i	−0.540809	−	0.392921i
$427$	−0.137090	−	0.421919i	−0.00663424	−	0.0204181i
$428$	−32.8640	+	23.8771i	−1.58854	+	1.15414i
$429$	9.96868	+	7.24267i	0.481293	+	0.349679i
$430$	−43.1415	−	31.3441i	−2.08047	−	1.51155i
$431$	19.3477	+	14.0569i	0.931946	+	0.677099i	0.946469	−	0.322796i	$-0.104623\pi$
$431$	19.3477	+	14.0569i	0.931946	+	0.677099i	−0.0145224	+	0.999895i	$0.504623\pi$
$432$	−6.94739	−	5.04757i	−0.334256	−	0.242852i
$433$	19.1897	−	13.9422i	0.922200	−	0.670017i	−0.0218707	−	0.999761i	$-0.506962\pi$
$433$	19.1897	−	13.9422i	0.922200	−	0.670017i	0.944071	+	0.329743i	$0.106962\pi$
$434$	−4.15228	−	12.7794i	−0.199316	−	0.613431i
$435$	−20.0751	−	14.5854i	−0.962527	−	0.699317i
$436$	8.92036	−	27.4540i	0.427208	−	1.31481i
$437$	11.6553			0.557547
$438$	−16.9779	+	12.3352i	−0.811237	+	0.589398i
$439$	6.05129	−	18.6240i	0.288812	−	0.888873i	−0.696418	−	0.717637i	$-0.745224\pi$
$439$	6.05129	−	18.6240i	0.288812	−	0.888873i	0.985230	−	0.171236i	$-0.0547762\pi$
$440$	8.18429	+	25.1887i	0.390171	+	1.20082i
$441$	−0.582954	−	1.79415i	−0.0277597	−	0.0854356i
$442$	84.5333			4.02084
$443$	10.0661	+	30.9804i	0.478257	+	1.47192i	0.841514	+	0.540235i	$0.181665\pi$
$443$	10.0661	+	30.9804i	0.478257	+	1.47192i	−0.363257	+	0.931689i	$0.618335\pi$
$444$	1.83773	+	1.33519i	0.0872149	+	0.0633653i
$445$	−27.3652	+	19.8820i	−1.29724	+	0.942497i
$446$	−4.34261	+	13.3652i	−0.205628	+	0.632859i
$447$	3.71225	−	11.4251i	0.175583	−	0.540390i
$448$	−11.6927			−0.552430
$449$	−17.5275	+	12.7345i	−0.827173	+	0.600976i	−0.918758	−	0.394821i	$-0.870807\pi$
$449$	−17.5275	+	12.7345i	−0.827173	+	0.600976i	0.0915852	+	0.995797i	$0.470807\pi$
$450$	−14.4082			−0.679207
$451$	12.8657	+	9.19897i	0.605821	+	0.433163i
$452$	−51.1127			−2.40414
$453$	17.8684	−	12.9821i	0.839530	−	0.609954i
$454$	1.79955			0.0844573
$455$	4.19160	−	12.9004i	0.196505	−	0.604781i
$456$	−7.58799	+	23.3534i	−0.355340	+	1.09363i
$457$	29.4240	−	21.3778i	1.37640	−	1.00001i	0.379192	−	0.925318i	$-0.376202\pi$
$457$	29.4240	−	21.3778i	1.37640	−	1.00001i	0.997206	−	0.0746945i	$-0.0237982\pi$
$458$	15.3162	+	11.1278i	0.715678	+	0.519970i
$459$	12.0599	+	37.1167i	0.562910	+	1.73246i
$460$	19.2360			0.896885
$461$	8.71606	+	26.8253i	0.405947	+	1.24938i	0.920102	+	0.391679i	$0.128106\pi$
$461$	8.71606	+	26.8253i	0.405947	+	1.24938i	−0.514155	+	0.857698i	$0.671894\pi$
$462$	−1.90293	−	5.85661i	−0.0885322	−	0.272474i
$463$	−10.8397	+	33.3611i	−0.503762	+	1.55042i	0.299079	+	0.954228i	$0.403321\pi$
$463$	−10.8397	+	33.3611i	−0.503762	+	1.55042i	−0.802841	+	0.596193i	$0.796679\pi$
$464$	11.0422	−	8.02261i	0.512620	−	0.372440i
$465$	17.2203			0.798573
$466$	−6.91603	+	21.2854i	−0.320379	+	0.986025i
$467$	−1.94227	−	1.41114i	−0.0898774	−	0.0652998i	0.541939	−	0.840418i	$-0.317690\pi$
$467$	−1.94227	−	1.41114i	−0.0898774	−	0.0652998i	−0.631816	+	0.775118i	$0.717690\pi$
$468$	−9.87083	−	30.3793i	−0.456279	−	1.40428i
$469$	−2.11395	+	1.53587i	−0.0976131	+	0.0709201i
$470$	−21.0012	−	15.2583i	−0.968713	−	0.703811i
$471$	5.13014	+	3.72727i	0.236385	+	0.171743i
$472$	−0.474126	−	0.344473i	−0.0218234	−	0.0158556i
$473$	−15.7197	−	11.4210i	−0.722791	−	0.525138i
$474$	−29.0632	+	21.1156i	−1.33491	+	0.969872i
$475$	6.22054	+	19.1449i	0.285418	+	0.878426i
$476$	−21.9316	−	15.9342i	−1.00523	−	0.730344i
$477$	6.72070	−	20.6842i	0.307720	−	0.947064i
$478$	−3.70743			−0.169574
$479$	31.8743	−	23.1580i	1.45637	−	1.05812i	0.472083	−	0.881554i	$-0.343502\pi$
$479$	31.8743	−	23.1580i	1.45637	−	1.05812i	0.984289	−	0.176562i	$-0.0564977\pi$
$480$	3.31151	−	10.1918i	0.151149	−	0.465189i
$481$	0.877987	+	2.70217i	0.0400328	+	0.123208i
$482$	9.16838	+	28.2174i	0.417608	+	1.28527i
$483$	−1.97514			−0.0898720
$484$	−5.42216	−	16.6877i	−0.246462	−	0.758532i
$485$	2.45024	+	1.78020i	0.111260	+	0.0808348i
$486$	30.0073	−	21.8016i	1.36116	−	0.988939i
$487$	7.51574	−	23.1311i	0.340571	−	1.04817i	−0.623342	−	0.781949i	$-0.714226\pi$
$487$	7.51574	−	23.1311i	0.340571	−	1.04817i	0.963913	−	0.266219i	$-0.0857745\pi$
$488$	−0.512302	+	1.57670i	−0.0231908	+	0.0713740i
$489$	3.01494			0.136340
$490$	−5.48422	+	3.98452i	−0.247752	+	0.180002i
$491$	−2.54298			−0.114763			−0.0573816	−	0.998352i	$-0.518275\pi$
$491$	−2.54298			−0.114763			−0.0573816	+	0.998352i	$0.518275\pi$
$492$	7.65317	+	22.9592i	0.345032	+	1.03508i
$493$	−62.0291			−2.79365
$494$	−56.2655	+	40.8793i	−2.53150	+	1.83924i
$495$	−13.3699			−0.600934
$496$	−2.92698	+	9.00833i	−0.131425	+	0.404486i
$497$	−1.71017	+	5.26336i	−0.0767116	+	0.236094i
$498$	11.2474	−	8.17173i	0.504009	−	0.366184i
$499$	17.0729	+	12.4042i	0.764286	+	0.555286i	0.900222	−	0.435431i	$-0.143404\pi$
$499$	17.0729	+	12.4042i	0.764286	+	0.555286i	−0.135936	+	0.990718i	$0.543404\pi$
$500$	−5.61239	−	17.2732i	−0.250994	−	0.772479i
$501$	−9.36856			−0.418556
$502$	−10.9015	−	33.5515i	−0.486560	−	1.49748i
$503$	−8.77907	−	27.0192i	−0.391440	−	1.20473i	−0.931700	−	0.363229i	$-0.881674\pi$
$503$	−8.77907	−	27.0192i	−0.391440	−	1.20473i	0.540260	−	0.841498i	$-0.318326\pi$
$504$	−2.17849	+	6.70469i	−0.0970375	+	0.298651i
$505$	25.7062	−	18.6766i	1.14391	−	0.831100i
$506$	10.9229			0.485583
$507$	−3.04845	+	9.38217i	−0.135387	+	0.416677i
$508$	25.3873	+	18.4449i	1.12638	+	0.818362i
$509$	5.37881	+	16.5543i	0.238412	+	0.733756i	0.996651	+	0.0817788i	$0.0260601\pi$
$509$	5.37881	+	16.5543i	0.238412	+	0.733756i	−0.758239	+	0.651977i	$0.773940\pi$
$510$	43.8008	−	31.8231i	1.93953	−	1.40915i
$511$	6.81005	+	4.94779i	0.301259	+	0.218878i
$512$	14.8386	+	10.7809i	0.655781	+	0.476453i
$513$	−25.9763	−	18.8729i	−1.14688	−	0.833258i
$514$	−10.5680	−	7.67807i	−0.466132	−	0.338665i
$515$	17.1493	−	12.4597i	0.755688	−	0.549039i
$516$	−9.18770	−	28.2768i	−0.404466	−	1.24482i
$517$	−7.65230	−	5.55972i	−0.336548	−	0.244516i
$518$	0.438781	−	1.35043i	0.0192789	−	0.0593345i
$519$	−2.13425			−0.0936833
$520$	−41.0087	+	29.7946i	−1.79835	+	1.30658i
$521$	−11.0034	+	33.8650i	−0.482068	+	1.48365i	0.354115	+	0.935202i	$0.384782\pi$
$521$	−11.0034	+	33.8650i	−0.482068	+	1.48365i	−0.836183	+	0.548451i	$0.815218\pi$
$522$	11.2875	+	34.7393i	0.494040	+	1.52050i
$523$	−0.125200	−	0.385326i	−0.00547462	−	0.0168491i	0.948282	−	0.317429i	$-0.102820\pi$
$523$	−0.125200	−	0.385326i	−0.00547462	−	0.0168491i	−0.953757	+	0.300580i	$0.902820\pi$
$524$	−29.8614			−1.30450
$525$	−1.05415	−	3.24435i	−0.0460070	−	0.141595i
$526$	31.5268	+	22.9056i	1.37464	+	0.998731i
$527$	34.8253	−	25.3020i	1.51701	−	1.10217i
$528$	−1.34139	+	4.12838i	−0.0583766	+	0.179665i
$529$	−6.02476	+	18.5423i	−0.261946	+	0.806187i
$530$	−78.1516			−3.39469
$531$	0.239345	−	0.173894i	0.0103867	−	0.00754637i
$532$	22.3033			0.966969
$533$	−9.13512	+	28.8590i	−0.395686	+	1.25002i
$534$	−29.3903			−1.27184
$535$	−26.3269	+	19.1276i	−1.13821	+	0.826957i
$536$	9.76468			0.421770
$537$	−2.76142	+	8.49878i	−0.119164	+	0.366749i
$538$	18.0096	−	55.4278i	0.776449	−	2.38966i
$539$	−1.99831	+	1.45186i	−0.0860733	+	0.0625359i
$540$	−42.8716	−	31.1481i	−1.84490	−	1.34040i
$541$	−0.623567	−	1.91914i	−0.0268093	−	0.0825104i	0.936757	−	0.349981i	$-0.113812\pi$
$541$	−0.623567	−	1.91914i	−0.0268093	−	0.0825104i	−0.963566	+	0.267471i	$0.913812\pi$
$542$	−40.5739			−1.74280
$543$	−6.19685	−	19.0720i	−0.265932	−	0.818456i
$544$	−8.27793	−	25.4769i	−0.354913	−	1.09231i
$545$	7.14595	−	21.9930i	0.306099	−	0.942076i
$546$	9.53493	−	6.92753i	0.408057	−	0.296471i
$547$	−4.69698			−0.200828			−0.100414	−	0.994946i	$-0.532017\pi$
$547$	−4.69698			−0.200828			−0.100414	+	0.994946i	$0.532017\pi$
$548$	−8.81694	+	27.1358i	−0.376641	+	1.15918i
$549$	−0.677067	−	0.491918i	−0.0288965	−	0.0209946i
$550$	5.82967	+	17.9419i	0.248578	+	0.765045i
$551$	41.2867	−	29.9965i	1.75887	−	1.27789i
$552$	5.97141	+	4.33848i	0.254160	+	0.184658i
$553$	11.6576	+	8.46972i	0.495731	+	0.360169i
$554$	34.4158	+	25.0045i	1.46219	+	1.06234i
$555$	1.47218	+	1.06960i	0.0624904	+	0.0454020i
$556$	−7.13698	+	5.18532i	−0.302676	+	0.219907i
$557$	−6.02645	−	18.5475i	−0.255349	−	0.785883i	−0.993761	−	0.111533i	$-0.964424\pi$
$557$	−6.02645	−	18.5475i	−0.255349	−	0.785883i	0.738412	−	0.674350i	$-0.235576\pi$
$558$	−20.5075	−	14.8996i	−0.868154	−	0.630751i
$559$	11.4918	−	35.3681i	0.486052	−	1.49591i
$560$	4.77849			0.201928
$561$	15.9599	−	11.5955i	0.673827	−	0.489564i
$562$	18.7395	−	57.6742i	0.790477	−	2.43284i
$563$	−0.753678	−	2.31958i	−0.0317638	−	0.0977588i	0.933918	−	0.357488i	$-0.116367\pi$
$563$	−0.753678	−	2.31958i	−0.0317638	−	0.0977588i	−0.965681	+	0.259729i	$0.916367\pi$
$564$	−4.47255	−	13.7651i	−0.188328	−	0.579615i
$565$	−40.9456			−1.72259
$566$	−2.27713	−	7.00828i	−0.0957148	−	0.294580i
$567$	−0.176552	−	0.128272i	−0.00741448	−	0.00538693i
$568$	16.7315	−	12.1562i	0.702039	−	0.510061i
$569$	2.71160	−	8.34546i	0.113676	−	0.349860i	−0.877992	−	0.478675i	$-0.841117\pi$
$569$	2.71160	−	8.34546i	0.113676	−	0.349860i	0.991669	+	0.128815i	$0.0411173\pi$
$570$	−13.7646	+	42.3630i	−0.576535	+	1.77439i
$571$	42.5060			1.77882			0.889411	−	0.457109i	$-0.151115\pi$
$571$	42.5060			1.77882			0.889411	+	0.457109i	$0.151115\pi$
$572$	−33.8363	+	24.5835i	−1.41477	+	1.02789i
$573$	−14.8298			−0.619522
$574$	12.1708	−	8.98462i	0.507999	−	0.375011i
$575$	6.05090			0.252340
$576$	−17.8454	+	12.9654i	−0.743557	+	0.540226i
$577$	36.6143			1.52427			0.762136	−	0.647417i	$-0.224151\pi$
$577$	36.6143			1.52427			0.762136	+	0.647417i	$0.224151\pi$
$578$	29.4105	−	90.5162i	1.22332	−	3.76498i
$579$	−4.89611	+	15.0687i	−0.203475	+	0.626233i
$580$	68.1401	−	49.5067i	2.82936	−	2.05565i
$581$	−4.51148	−	3.27778i	−0.187168	−	0.135985i
$582$	0.813196	+	2.50276i	0.0337080	+	0.103743i
$583$	−28.4764			−1.17937
$584$	−9.72067	−	29.9172i	−0.402244	−	1.23798i
$585$	−7.90736	−	24.3364i	−0.326929	−	1.00618i
$586$	13.0298	−	40.1017i	0.538257	−	1.65658i
$587$	8.05889	−	5.85513i	0.332626	−	0.241667i	−0.408918	−	0.912571i	$-0.634094\pi$
$587$	8.05889	−	5.85513i	0.332626	−	0.241667i	0.741544	+	0.670904i	$0.234094\pi$
$588$	−3.77958			−0.155867
$589$	−10.9440	+	33.6821i	−0.450939	+	1.38785i
$590$	−0.860063	−	0.624872i	−0.0354082	−	0.0257256i
$591$	−5.06256	−	15.5810i	−0.208246	−	0.640915i
$592$	−0.809761	+	0.588326i	−0.0332810	+	0.0241800i
$593$	16.3710	+	11.8943i	0.672278	+	0.488438i	0.870787	−	0.491661i	$-0.163610\pi$
$593$	16.3710	+	11.8943i	0.672278	+	0.488438i	−0.198509	+	0.980099i	$0.563610\pi$
$594$	−24.3441	−	17.6870i	−0.998849	−	0.725707i
$595$	−17.5690	−	12.7646i	−0.720260	−	0.523299i
$596$	32.9881	+	23.9673i	1.35125	+	0.981737i
$597$	−19.3065	+	14.0270i	−0.790164	+	0.574088i
$598$	6.46013	+	19.8822i	0.264174	+	0.813045i
$599$	26.6861	+	19.3886i	1.09036	+	0.792195i	0.979460	−	0.201637i	$-0.0646260\pi$
$599$	26.6861	+	19.3886i	1.09036	+	0.792195i	0.110902	+	0.993831i	$0.464626\pi$
$600$	−3.93935	+	12.1241i	−0.160823	+	0.494963i
$601$	−2.56852			−0.104772			−0.0523861	−	0.998627i	$-0.516683\pi$
$601$	−2.56852			−0.104772			−0.0523861	+	0.998627i	$0.516683\pi$
$602$	−15.0357	+	10.9241i	−0.612809	+	0.445231i
$603$	−1.52325	+	4.68808i	−0.0620315	+	0.190913i
$604$	23.1662	+	71.2982i	0.942619	+	2.90108i
$605$	−4.34361	−	13.3682i	−0.176593	−	0.543496i
$606$	27.6085			1.12152
$607$	−7.13919	−	21.9722i	−0.289771	−	0.891822i	−0.984928	−	0.172965i	$-0.944665\pi$
$607$	−7.13919	−	21.9722i	−0.289771	−	0.891822i	0.695157	−	0.718858i	$-0.255335\pi$
$608$	17.8301	+	12.9543i	0.723106	+	0.525367i
$609$	−6.99657	+	5.08331i	−0.283515	+	0.205986i
$610$	−0.929313	+	2.86013i	−0.0376268	+	0.115803i
$611$	5.59418	−	17.2171i	0.226316	−	0.696530i
$612$	−51.1403			−2.06723
$613$	−1.71838	+	1.24848i	−0.0694047	+	0.0504255i	−0.621947	−	0.783060i	$-0.713658\pi$
$613$	−1.71838	+	1.24848i	−0.0694047	+	0.0504255i	0.552542	+	0.833485i	$0.313658\pi$
$614$	43.8475			1.76954
$615$	6.13083	+	18.3922i	0.247219	+	0.741646i
$616$	9.23052			0.371908
$617$	−34.1181	+	24.7883i	−1.37354	+	0.997937i	−0.376092	+	0.926582i	$0.622732\pi$
$617$	−34.1181	+	24.7883i	−1.37354	+	0.997937i	−0.997451	+	0.0713552i	$0.977268\pi$
$618$	18.4183			0.740894
$619$	5.09776	−	15.6893i	0.204896	−	0.630606i	−0.794821	−	0.606844i	$-0.792435\pi$
$619$	5.09776	−	15.6893i	0.204896	−	0.630606i	0.999718	−	0.0237625i	$-0.00756454\pi$
$620$	−18.0621	+	55.5895i	−0.725392	+	2.23253i
$621$	−7.80821	+	5.67300i	−0.313333	+	0.227650i
$622$	14.0053	+	10.1755i	0.561562	+	0.407999i
$623$	3.64293	+	11.2118i	0.145951	+	0.449191i
$624$	−8.30794			−0.332584
$625$	−9.49086	−	29.2099i	−0.379635	−	1.16840i
$626$	18.5204	+	57.0000i	0.740225	+	2.27818i
$627$	−5.01546	+	15.4360i	−0.200298	+	0.616455i
$628$	−17.4130	+	12.6513i	−0.694856	+	0.504842i
$629$	4.54881			0.181373
$630$	−3.95177	+	12.1623i	−0.157442	+	0.484557i
$631$	5.26733	+	3.82694i	0.209689	+	0.152348i	0.687673	−	0.726021i	$-0.258632\pi$
$631$	5.26733	+	3.82694i	0.209689	+	0.152348i	−0.477984	+	0.878369i	$0.658632\pi$
$632$	−16.6400	−	51.2127i	−0.661905	−	2.03713i
$633$	6.24048	−	4.53398i	0.248037	−	0.180209i
$634$	−19.7279	−	14.3331i	−0.783493	−	0.569241i
$635$	20.3373	+	14.7759i	0.807063	+	0.586365i
$636$	−35.2519	−	25.6120i	−1.39783	−	1.01558i
$637$	−3.82457	−	2.77872i	−0.151535	−	0.110097i
$638$	38.6924	−	28.1117i	1.53185	−	1.11295i
$639$	3.22620	+	9.92922i	0.127626	+	0.392794i
$640$	47.6939	+	34.6516i	1.88527	+	1.36973i
$641$	2.77360	−	8.53625i	0.109550	−	0.337162i	−0.881221	−	0.472704i	$-0.843278\pi$
$641$	2.77360	−	8.53625i	0.109550	−	0.337162i	0.990771	+	0.135543i	$0.0432778\pi$
$642$	−28.2750			−1.11593
$643$	−16.2817	+	11.8294i	−0.642088	+	0.466504i	−0.860567	−	0.509337i	$-0.829891\pi$
$643$	−16.2817	+	11.8294i	−0.642088	+	0.466504i	0.218479	+	0.975842i	$0.429891\pi$
$644$	2.07169	−	6.37602i	0.0816362	−	0.251250i
$645$	−7.36012	−	22.6521i	−0.289804	−	0.891926i
$646$	34.4080	+	105.897i	1.35376	+	4.16645i
$647$	−45.0437			−1.77085			−0.885426	−	0.464780i	$-0.846133\pi$
$647$	−45.0437			−1.77085			−0.885426	+	0.464780i	$0.846133\pi$
$648$	0.252010	+	0.775607i	0.00989989	+	0.0304687i
$649$	−0.313385	−	0.227687i	−0.0123014	−	0.00893751i
$650$	−29.2105	+	21.2227i	−1.14573	+	0.832423i
$651$	1.85460	−	5.70789i	0.0726877	−	0.223710i
$652$	−3.16232	+	9.73263i	−0.123846	+	0.381159i
$653$	26.8752			1.05171			0.525855	−	0.850574i	$-0.323746\pi$
$653$	26.8752			1.05171			0.525855	+	0.850574i	$0.323746\pi$
$654$	16.2554	−	11.8102i	0.635636	−	0.461817i
$655$	−23.9215			−0.934691
$656$	−10.6635	+	0.0809953i	−0.416338	+	0.00316234i
$657$	15.8798			0.619529
$658$	−7.31933	+	5.31781i	−0.285337	+	0.207310i
$659$	29.9097			1.16512			0.582559	−	0.812788i	$-0.302051\pi$
$659$	29.9097			1.16512			0.582559	+	0.812788i	$0.302051\pi$
$660$	−8.27759	+	25.4758i	−0.322205	+	0.991644i
$661$	−10.4664	+	32.2122i	−0.407094	+	1.25291i	0.512039	+	0.858962i	$0.328890\pi$
$661$	−10.4664	+	32.2122i	−0.407094	+	1.25291i	−0.919134	+	0.393946i	$0.871110\pi$
$662$	63.0348	−	45.7975i	2.44992	−	1.77997i
$663$	30.5457	+	22.1927i	1.18630	+	0.861895i
$664$	6.43968	+	19.8193i	0.249908	+	0.769138i
$665$	17.8668			0.692844
$666$	−0.827751	−	2.54755i	−0.0320747	−	0.0987157i
$667$	−4.74034	−	14.5893i	−0.183547	−	0.564898i
$668$	9.82653	−	30.2430i	0.380200	−	1.17014i
$669$	−5.07797	+	3.68936i	−0.196326	+	0.142639i
$670$	17.7131			0.684316
$671$	−0.338618	+	1.04216i	−0.0130722	+	0.0402321i
$672$	−3.02155	−	2.19528i	−0.116559	−	0.0846848i
$673$	8.87279	+	27.3076i	0.342021	+	1.05263i	0.963159	+	0.268931i	$0.0866703\pi$
$673$	8.87279	+	27.3076i	0.342021	+	1.05263i	−0.621139	+	0.783701i	$0.713330\pi$
$674$	5.40071	−	3.92385i	0.208028	−	0.151141i
$675$	−13.4857	−	9.79796i	−0.519066	−	0.377124i
$676$	−27.0894	−	19.6816i	−1.04190	−	0.756985i
$677$	0.431753	+	0.313687i	0.0165936	+	0.0120560i	0.596051	−	0.802946i	$-0.296736\pi$
$677$	0.431753	+	0.313687i	0.0165936	+	0.0120560i	−0.579458	+	0.815002i	$0.696736\pi$
$678$	−28.7824	−	20.9116i	−1.10538	−	0.803106i
$679$	0.853957	−	0.620436i	0.0327719	−	0.0238101i
$680$	25.0780	+	77.1822i	0.961698	+	2.95980i
$681$	0.650260	+	0.472442i	0.0249180	+	0.0181040i
$682$	−10.2563	+	31.5657i	−0.392735	+	1.20871i
$683$	19.5602			0.748451			0.374225	−	0.927338i	$-0.377909\pi$
$683$	19.5602			0.748451			0.374225	+	0.927338i	$0.377909\pi$
$684$	34.0391	−	24.7308i	1.30152	−	0.945607i
$685$	−7.06311	+	21.7380i	−0.269867	+	0.830567i
$686$	0.730075	+	2.24694i	0.0278744	+	0.0857885i
$687$	2.61300	+	8.04199i	0.0996922	+	0.306821i
$688$	13.1008			0.499465
$689$	−16.8418	−	51.8337i	−0.641621	−	1.97471i
$690$	10.8321	+	7.86999i	0.412371	+	0.299605i
$691$	−15.3734	+	11.1694i	−0.584832	+	0.424905i	−0.840463	−	0.541869i	$-0.817717\pi$
$691$	−15.3734	+	11.1694i	−0.584832	+	0.424905i	0.255631	+	0.966774i	$0.417717\pi$
$692$	2.23858	−	6.88965i	0.0850981	−	0.261905i
$693$	−1.43992	+	4.43163i	−0.0546981	+	0.168344i
$694$	11.8250			0.448871
$695$	−5.71732	+	4.15388i	−0.216870	+	0.157566i
$696$	32.3183			1.22502
$697$	39.4225	+	28.1872i	1.49324	+	1.06767i
$698$	7.82438			0.296157
$699$	−8.08717	+	5.87568i	−0.305885	+	0.222238i
$700$	11.5789			0.437640
$701$	−2.38944	+	7.35395i	−0.0902481	+	0.277755i	−0.985986	−	0.166827i	$-0.946648\pi$
$701$	−2.38944	+	7.35395i	−0.0902481	+	0.277755i	0.895738	+	0.444582i	$0.146648\pi$
$702$	17.7966	−	54.7724i	0.671691	−	2.06725i
$703$	−3.02770	+	2.19975i	−0.114192	+	0.0829651i
$704$	23.3657	+	16.9762i	0.880629	+	0.639814i
$705$	−3.58289	−	11.0270i	−0.134939	−	0.415301i
$706$	11.1375			0.419164
$707$	−3.42208	−	10.5321i	−0.128701	−	0.396100i
$708$	−0.183165	−	0.563723i	−0.00688375	−	0.0211860i
$709$	9.64254	−	29.6767i	0.362133	−	1.11453i	−0.589623	−	0.807678i	$-0.700724\pi$
$709$	9.64254	−	29.6767i	0.362133	−	1.11453i	0.951757	−	0.306853i	$-0.0992761\pi$
$710$	30.3509	−	22.0512i	1.13905	−	0.827568i
$711$	27.1833			1.01945
$712$	13.6136	−	41.8983i	0.510190	−	1.57020i
$713$	8.61243	+	6.25730i	0.322538	+	0.234338i
$714$	−5.83088	−	17.9456i	−0.218215	−	0.671598i
$715$	−27.1057	+	19.6934i	−1.01370	+	0.736493i
$716$	−24.5388	−	17.8285i	−0.917057	−	0.666281i
$717$	−1.33966	−	0.973321i	−0.0500306	−	0.0363494i
$718$	−47.5608	−	34.5549i	−1.77495	−	1.28958i
$719$	28.1932	+	20.4836i	1.05143	+	0.763909i	0.972484	−	0.232970i	$-0.0748445\pi$
$719$	28.1932	+	20.4836i	1.05143	+	0.763909i	0.0789460	+	0.996879i	$0.474845\pi$
$720$	7.29290	−	5.29860i	0.271790	−	0.197467i
$721$	−2.28296	−	7.02623i	−0.0850219	−	0.261671i
$722$	−37.7965	−	27.4608i	−1.40664	−	1.02198i
$723$	−4.09503	+	12.6032i	−0.152296	+	0.468718i
$724$	68.0666			2.52967
$725$	21.4342	−	15.5729i	0.796047	−	0.578362i
$726$	3.77409	−	11.6155i	0.140070	−	0.431090i
$727$	8.96308	+	27.5855i	0.332422	+	1.02309i	0.967978	+	0.251035i	$0.0807710\pi$
$727$	8.96308	+	27.5855i	0.332422	+	1.02309i	−0.635556	+	0.772055i	$0.719229\pi$
$728$	5.45920	+	16.8017i	0.202331	+	0.622712i
$729$	15.9119			0.589330
$730$	−17.6333	−	54.2696i	−0.652636	−	2.00861i
$731$	−48.1677	−	34.9959i	−1.78155	−	1.29437i
$732$	−1.35651	+	0.985565i	−0.0501382	+	0.0364275i
$733$	1.48116	−	4.55853i	0.0547078	−	0.168373i	−0.919969	−	0.391991i	$-0.871787\pi$
$733$	1.48116	−	4.55853i	0.0547078	−	0.168373i	0.974677	+	0.223617i	$0.0717866\pi$
$734$	−6.96855	+	21.4470i	−0.257214	+	0.791623i
$735$	−3.02776			−0.111681
$736$	5.35955	−	3.89394i	0.197556	−	0.143533i
$737$	6.45420			0.237743
$738$	8.61242	−	27.2078i	0.317028	−	1.00153i
$739$	10.2889			0.378483			0.189241	−	0.981931i	$-0.439397\pi$
$739$	10.2889			0.378483			0.189241	+	0.981931i	$0.439397\pi$
$740$	−4.99695	+	3.63050i	−0.183692	+	0.133460i
$741$	−31.0634			−1.14114
$742$	−8.41682	+	25.9043i	−0.308991	+	0.950977i
$743$	−10.8790	+	33.4820i	−0.399110	+	1.22834i	0.526604	+	0.850111i	$0.323465\pi$
$743$	−10.8790	+	33.4820i	−0.399110	+	1.22834i	−0.925714	+	0.378224i	$0.876535\pi$
$744$	−18.1446	+	13.1828i	−0.665214	+	0.483306i
$745$	26.4262	+	19.1998i	0.968182	+	0.703426i
$746$	−25.6921	−	79.0720i	−0.940653	−	2.89503i
$747$	−10.5199			−0.384904
$748$	20.6919	+	63.6830i	0.756570	+	2.32848i
$749$	3.50470	+	10.7864i	0.128059	+	0.394125i
$750$	3.90650	−	12.0230i	0.142645	−	0.439017i
$751$	−18.3562	+	13.3366i	−0.669827	+	0.486658i	−0.869967	−	0.493109i	$-0.835860\pi$
$751$	−18.3562	+	13.3366i	−0.669827	+	0.486658i	0.200140	+	0.979767i	$0.435860\pi$
$752$	6.37746			0.232562
$753$	4.86914	−	14.9857i	0.177442	−	0.546109i
$754$	74.0536	+	53.8031i	2.69687	+	1.95939i
$755$	18.5581	+	57.1159i	0.675397	+	2.07866i
$756$	−14.9416	+	10.8557i	−0.543421	+	0.394819i
$757$	14.5046	+	10.5382i	0.527178	+	0.383017i	0.819301	−	0.573363i	$-0.194362\pi$
$757$	14.5046	+	10.5382i	0.527178	+	0.383017i	−0.292123	+	0.956381i	$0.594362\pi$
$758$	45.9486	+	33.3836i	1.66893	+	1.21255i
$759$	3.94694	+	2.86762i	0.143265	+	0.104088i
$760$	−54.0163	−	39.2452i	−1.95938	−	1.42357i
$761$	−14.7713	+	10.7319i	−0.535458	+	0.389033i	−0.822395	−	0.568916i	$-0.807363\pi$
$761$	−14.7713	+	10.7319i	−0.535458	+	0.389033i	0.286938	+	0.957949i	$0.407363\pi$
$762$	6.74964	+	20.7733i	0.244514	+	0.752536i
$763$	−6.52023	−	4.73723i	−0.236048	−	0.171499i
$764$	15.5547	−	47.8724i	0.562749	−	1.73196i
$765$	−40.9677			−1.48119
$766$	61.6278	−	44.7752i	2.22670	−	1.61779i
$767$	0.229099	−	0.705094i	0.00827228	−	0.0254595i
$768$	8.20318	+	25.2468i	0.296007	+	0.911015i
$769$	0.786381	+	2.42023i	0.0283576	+	0.0872758i	0.964234	−	0.265054i	$-0.0853897\pi$
$769$	0.786381	+	2.42023i	0.0283576	+	0.0872758i	−0.935876	+	0.352329i	$0.885390\pi$
$770$	16.7441			0.603417
$771$	−1.80294	−	5.54886i	−0.0649311	−	0.199837i
$772$	−43.5082	−	31.6106i	−1.56590	−	1.13769i
$773$	−21.2506	+	15.4395i	−0.764330	+	0.555319i	−0.900236	−	0.435403i	$-0.856606\pi$
$773$	−21.2506	+	15.4395i	−0.764330	+	0.555319i	0.135905	+	0.990722i	$0.456606\pi$
$774$	−10.8343	+	33.3444i	−0.389430	+	1.19854i
$775$	−5.68164	+	17.4863i	−0.204090	+	0.628126i
$776$	−3.94457			−0.141602
$777$	0.513083	−	0.372777i	0.0184068	−	0.0133733i
$778$	−37.6051			−1.34821
$779$	−39.8707	+	0.302841i	−1.42851	+	0.0108504i
$780$	−51.2675			−1.83567
$781$	11.0591	−	8.03491i	0.395726	−	0.287512i
$782$	33.4696			1.19687
$783$	−13.0589	+	40.1911i	−0.466686	+	1.43631i
$784$	0.514637	−	1.58389i	0.0183799	−	0.0565675i
$785$	−13.9493	+	10.1348i	−0.497872	+	0.361725i
$786$	−16.8154	−	12.2171i	−0.599787	−	0.435771i
$787$	6.56150	+	20.1942i	0.233892	+	0.719846i	0.997266	+	0.0738894i	$0.0235412\pi$
$787$	6.56150	+	20.1942i	0.233892	+	0.719846i	−0.763374	+	0.645956i	$0.776459\pi$
$788$	55.6074			1.98093
$789$	5.37861	+	16.5536i	0.191483	+	0.589325i
$790$	−30.1849	−	92.8997i	−1.07393	−	3.30522i
$791$	−4.40978	+	13.5719i	−0.156794	+	0.482562i
$792$	14.0876	−	10.2352i	0.500579	−	0.363692i
$793$	−2.09724			−0.0744751
$794$	2.73964	−	8.43176i	0.0972263	−	0.299232i
$795$	−28.2397	−	20.5173i	−1.00156	−	0.727675i
$796$	−25.0308	−	77.0368i	−0.887192	−	2.73050i
$797$	3.66552	−	2.66316i	0.129840	−	0.0943340i	−0.520970	−	0.853575i	$-0.674430\pi$
$797$	3.66552	−	2.66316i	0.129840	−	0.0943340i	0.650810	+	0.759241i	$0.274430\pi$
$798$	12.5593	+	9.12488i	0.444595	+	0.323017i
$799$	−23.4479	−	17.0359i	−0.829527	−	0.602687i
$800$	9.25660	+	6.72531i	0.327270	+	0.237776i
$801$	17.9919	+	13.0719i	0.635714	+	0.461873i
$802$	−35.5927	+	25.8596i	−1.25682	+	0.913133i
$803$	−6.42511	−	19.7745i	−0.226737	−	0.697825i
$804$	7.98985	+	5.80497i	0.281780	+	0.204725i
$805$	1.65960	−	5.10772i	0.0584932	−	0.180024i
$806$	−63.5228			−2.23750
$807$	21.0593	−	15.3005i	0.741322	−	0.538602i
$808$	−12.7883	+	39.3582i	−0.449889	+	1.38462i
$809$	−10.9648	−	33.7462i	−0.385502	−	1.18645i	−0.936116	−	0.351692i	$-0.885606\pi$
$809$	−10.9648	−	33.7462i	−0.385502	−	1.18645i	0.550614	−	0.834760i	$-0.314394\pi$
$810$	0.457145	+	1.40695i	0.0160624	+	0.0494351i
$811$	−4.01703			−0.141057			−0.0705285	−	0.997510i	$-0.522469\pi$
$811$	−4.01703			−0.141057			−0.0705285	+	0.997510i	$0.522469\pi$
$812$	−9.07100	−	27.9177i	−0.318330	−	0.979718i
$813$	−14.6612	−	10.6520i	−0.514191	−	0.373581i
$814$	−2.83745	+	2.06153i	−0.0994526	+	0.0722566i
$815$	−2.53329	+	7.79665i	−0.0887371	+	0.273105i
$816$	−4.11025	+	12.6500i	−0.143887	+	0.442840i
$817$	48.9840			1.71373
$818$	−33.4426	+	24.2975i	−1.16929	+	0.849541i
$819$	−8.91820			−0.311627
$820$	−65.8031	+	0.499814i	−2.29794	+	0.0174543i
$821$	−14.7792			−0.515797			−0.257898	−	0.966172i	$-0.583030\pi$
$821$	−14.7792			−0.515797			−0.257898	+	0.966172i	$0.583030\pi$
$822$	−16.0669	+	11.6733i	−0.560399	+	0.407154i
$823$	−10.4729			−0.365063			−0.182532	−	0.983200i	$-0.558429\pi$
$823$	−10.4729			−0.365063			−0.182532	+	0.983200i	$0.558429\pi$
$824$	−8.53138	+	26.2569i	−0.297205	+	0.914702i
$825$	−2.60381	+	8.01369i	−0.0906529	+	0.279001i
$826$	−0.299749	+	0.217780i	−0.0104296	+	0.00757755i
$827$	−3.07271	−	2.23246i	−0.106849	−	0.0776301i	0.533078	−	0.846066i	$-0.321035\pi$
$827$	−3.07271	−	2.23246i	−0.106849	−	0.0776301i	−0.639927	+	0.768436i	$0.721035\pi$
$828$	−3.90820	−	12.0282i	−0.135819	−	0.418009i
$829$	−48.5895			−1.68758			−0.843791	−	0.536672i	$-0.819681\pi$
$829$	−48.5895			−1.68758			−0.843791	+	0.536672i	$0.819681\pi$
$830$	11.6816	+	35.9521i	0.405473	+	1.24792i
$831$	5.87147	+	18.0705i	0.203679	+	0.626860i
$832$	−17.0814	+	52.5712i	−0.592192	+	1.82258i
$833$	−6.12315	+	4.44873i	−0.212155	+	0.154139i
$834$	−6.14041			−0.212625
$835$	7.87187	−	24.2271i	0.272417	−	0.838415i
$836$	−44.5688	−	32.3812i	−1.54145	−	1.11993i
$837$	−9.06248	−	27.8915i	−0.313245	−	0.964070i
$838$	33.4811	−	24.3255i	1.15659	−	0.840310i
$839$	−31.2419	−	22.6985i	−1.07859	−	0.783641i	−0.101153	−	0.994871i	$-0.532253\pi$
$839$	−31.2419	−	22.6985i	−1.07859	−	0.783641i	−0.977436	+	0.211230i	$0.932253\pi$
$840$	9.15378	+	6.65061i	0.315835	+	0.229468i
$841$	−30.8778	−	22.4340i	−1.06475	−	0.773587i
$842$	−16.8187	−	12.2195i	−0.579611	−	0.421112i
$843$	21.9128	−	15.9206i	0.754716	−	0.548333i
$844$	8.09074	+	24.9007i	0.278495	+	0.857118i
$845$	−21.7009	−	15.7666i	−0.746533	−	0.542388i
$846$	−5.27409	+	16.2320i	−0.181327	+	0.558067i
$847$	−4.89887			−0.168327
$848$	15.5331	−	11.2854i	0.533407	−	0.387543i
$849$	1.01707	−	3.13023i	0.0349058	−	0.107429i
$850$	17.8631	+	54.9769i	0.612699	+	1.88569i
$851$	0.347625	+	1.06988i	0.0119164	+	0.0366751i
$852$	20.9171			0.716607
$853$	5.33187	+	16.4098i	0.182560	+	0.561862i	0.999898	−	0.0142971i	$-0.00455105\pi$
$853$	5.33187	+	16.4098i	0.182560	+	0.561862i	−0.817338	+	0.576159i	$0.804551\pi$
$854$	0.847940	+	0.616064i	0.0290159	+	0.0210813i
$855$	27.2681	−	19.8115i	0.932551	−	0.677538i
$856$	13.0970	−	40.3085i	0.447647	−	1.37772i
$857$	14.7382	−	45.3594i	0.503446	−	1.54945i	−0.299922	−	0.953964i	$-0.596960\pi$
$857$	14.7382	−	45.3594i	0.503446	−	1.54945i	0.803367	−	0.595484i	$-0.203040\pi$
$858$	−29.1115			−0.993851
$859$	−7.23615	+	5.25737i	−0.246894	+	0.179379i	−0.704349	−	0.709854i	$-0.748761\pi$
$859$	−7.23615	+	5.25737i	−0.246894	+	0.179379i	0.457455	+	0.889233i	$0.348761\pi$
$860$	80.8439			2.75675
$861$	6.75661	−	0.0513205i	0.230265	−	0.00174900i
$862$	−56.5011			−1.92443
$863$	−5.20626	+	3.78257i	−0.177223	+	0.128760i	−0.672860	−	0.739769i	$-0.734935\pi$
$863$	−5.20626	+	3.78257i	−0.177223	+	0.128760i	0.495637	+	0.868530i	$0.334935\pi$
$864$	−18.2502			−0.620884
$865$	1.79329	−	5.51918i	0.0609738	−	0.187658i
$866$	−17.3172	+	53.2970i	−0.588464	+	1.81111i
$867$	34.3908	−	24.9864i	1.16797	−	0.848582i
$868$	16.4805	+	11.9738i	0.559386	+	0.406418i
$869$	−10.9986	−	33.8503i	−0.373103	−	1.14829i
$870$	58.6253			1.98758
$871$	3.81720	+	11.7481i	0.129341	+	0.398070i
$872$	9.30698	+	28.6439i	0.315174	+	0.970006i
$873$	0.615336	−	1.89381i	0.0208260	−	0.0640957i
$874$	−22.2774	+	16.1855i	−0.753545	+	0.547483i
$875$	−5.07074			−0.171422
$876$	9.83149	−	30.2582i	0.332175	−	1.02233i
$877$	0.0235870	+	0.0171369i	0.000796475	+	0.000578673i	0.588183	−	0.808728i	$-0.299843\pi$
$877$	0.0235870	+	0.0171369i	0.000796475	+	0.000578673i	−0.587387	+	0.809306i	$0.699843\pi$
$878$	14.2966	+	44.0004i	0.482487	+	1.48494i
$879$	15.2363	−	11.0698i	0.513906	−	0.373375i
$880$	−9.54891	−	6.93769i	−0.321894	−	0.233870i
$881$	−23.8387	−	17.3198i	−0.803147	−	0.583520i	0.108689	−	0.994076i	$-0.465335\pi$
$881$	−23.8387	−	17.3198i	−0.803147	−	0.583520i	−0.911836	+	0.410556i	$0.865335\pi$
$882$	3.60574	+	2.61972i	0.121412	+	0.0882106i
$883$	20.5234	+	14.9112i	0.690669	+	0.501800i	0.876880	−	0.480710i	$-0.159621\pi$
$883$	20.5234	+	14.9112i	0.690669	+	0.501800i	−0.186211	+	0.982510i	$0.559621\pi$
$884$	−103.680	+	75.3279i	−3.48714	+	2.53355i
$885$	−0.146730	−	0.451589i	−0.00493228	−	0.0151800i
$886$	−62.2621	−	45.2360i	−2.09173	−	1.51973i
$887$	−17.2685	+	53.1471i	−0.579820	+	1.78450i	0.0393237	+	0.999227i	$0.487480\pi$
$887$	−17.2685	+	53.1471i	−0.579820	+	1.78450i	−0.619144	+	0.785277i	$0.712520\pi$
$888$	−2.37002			−0.0795325
$889$	7.08797	−	5.14971i	0.237723	−	0.172716i
$890$	24.6950	−	76.0033i	0.827777	−	2.54764i
$891$	0.166572	+	0.512656i	0.00558037	+	0.0171746i
$892$	−6.58355	−	20.2621i	−0.220434	−	0.678425i
$893$	23.8453			0.797953
$894$	8.77045	+	26.9927i	0.293328	+	0.902770i
$895$	−19.6576	−	14.2821i	−0.657081	−	0.477398i
$896$	16.6223	−	12.0768i	0.555311	−	0.403457i
$897$	−2.88540	+	8.88034i	−0.0963407	+	0.296506i
$898$	15.8172	−	48.6803i	0.527826	−	1.62448i
$899$	46.6120			1.55460
$900$	17.6716	−	12.8392i	0.589053	−	0.427972i
$901$	−87.2566			−2.90694
$902$	−37.3654	+	0.283813i	−1.24413	+	0.00944992i
$903$	−8.30099			−0.276240
$904$	43.1433	−	31.3454i	1.43492	−	1.04253i
$905$	54.5270			1.81254
$906$	−16.1248	+	49.6271i	−0.535711	+	1.64875i
$907$	−11.9956	+	36.9186i	−0.398306	+	1.22586i	0.528050	+	0.849213i	$0.322923\pi$
$907$	−11.9956	+	36.9186i	−0.398306	+	1.22586i	−0.926357	+	0.376648i	$0.877077\pi$
$908$	−2.20715	+	1.60359i	−0.0732469	+	0.0532170i
$909$	−16.9012	−	12.2794i	−0.560577	−	0.407283i
$910$	9.90296	+	30.4782i	0.328280	+	1.01034i
$911$	49.4230			1.63746			0.818728	−	0.574181i	$-0.194679\pi$
$911$	49.4230			1.63746			0.818728	+	0.574181i	$0.194679\pi$
$912$	−3.38162	−	10.4075i	−0.111977	−	0.344628i
$913$	4.25646	+	13.1000i	0.140868	+	0.433548i
$914$	−26.5529	+	81.7214i	−0.878292	+	2.70311i
$915$	−1.08668	+	0.789520i	−0.0359246	+	0.0261007i
$916$	−28.7013			−0.948319
$917$	−2.57631	+	7.92908i	−0.0850774	+	0.261841i
$918$	−74.5943	−	54.1959i	−2.46198	−	1.78873i
$919$	9.05907	+	27.8810i	0.298831	+	0.919708i	0.981908	+	0.189361i	$0.0606416\pi$
$919$	9.05907	+	27.8810i	0.298831	+	0.919708i	−0.683076	+	0.730347i	$0.739358\pi$
$920$	−16.2368	+	11.7967i	−0.535310	+	0.388926i
$921$	15.8441	+	11.5114i	0.522080	+	0.379313i
$922$	−53.9114	−	39.1689i	−1.77548	−	1.28996i
$923$	21.1661	+	15.3780i	0.696689	+	0.506174i
$924$	7.55278	+	5.48742i	0.248468	+	0.180523i
$925$	−1.57185	+	1.14201i	−0.0516820	+	0.0375492i
$926$	−25.6095	−	78.8180i	−0.841581	−	2.59012i
$927$	−11.2752	−	8.19193i	−0.370327	−	0.269058i
$928$	8.96360	−	27.5871i	0.294245	−	0.905592i
$929$	0.247469			0.00811920			0.00405960	−	0.999992i	$-0.498708\pi$
$929$	0.247469			0.00811920			0.00405960	+	0.999992i	$0.498708\pi$
$930$	−32.9142	+	23.9136i	−1.07930	+	0.784158i
$931$	1.92423	−	5.92216i	0.0630640	−	0.194091i
$932$	−10.4850	−	32.2694i	−0.343446	−	1.05702i
$933$	2.38936	+	7.35370i	0.0782242	+	0.240749i
$934$	5.67200			0.185594
$935$	16.5759	+	51.0154i	0.542090	+	1.66838i
$936$	26.9622	+	19.5892i	0.881288	+	0.640293i
$937$	−24.1189	+	17.5234i	−0.787929	+	0.572464i	−0.907348	−	0.420380i	$-0.861897\pi$
$937$	−24.1189	+	17.5234i	−0.787929	+	0.572464i	0.119419	+	0.992844i	$0.461897\pi$
$938$	1.90767	−	5.87122i	0.0622878	−	0.191702i
$939$	−8.27210	+	25.4589i	−0.269950	+	0.830820i
$940$	39.3546			1.28361
$941$	5.58121	−	4.05499i	0.181942	−	0.132189i	−0.493086	−	0.869980i	$-0.664131\pi$
$941$	5.58121	−	4.05499i	0.181942	−	0.132189i	0.675029	+	0.737792i	$0.264131\pi$
$942$	−14.9816			−0.488125
$943$	−3.61691	+	11.4263i	−0.117783	+	0.372091i
$944$	0.261176			0.00850056
$945$	−11.9695	+	8.69634i	−0.389367	+	0.282892i
$946$	45.9061			1.49254
$947$	−12.7108	+	39.1198i	−0.413045	+	1.27122i	0.500942	+	0.865481i	$0.332987\pi$
$947$	−12.7108	+	39.1198i	−0.413045	+	1.27122i	−0.913988	+	0.405742i	$0.867013\pi$
$948$	16.8297	−	51.7966i	0.546604	−	1.68227i
$949$	32.1941	−	23.3904i	1.04506	−	0.759283i
$950$	−38.4759	−	27.9543i	−1.24832	−	0.906959i
$951$	−3.36565	−	10.3584i	−0.109139	−	0.335894i
$952$	28.2839			0.916685
$953$	−16.9071	−	52.0347i	−0.547674	−	1.68557i	−0.714545	−	0.699589i	$-0.753366\pi$
$953$	−16.9071	−	52.0347i	−0.547674	−	1.68557i	0.166871	−	0.985979i	$-0.446634\pi$
$954$	15.8781	+	48.8679i	0.514074	+	1.58216i
$955$	12.4606	−	38.3498i	0.403216	−	1.24097i
$956$	4.54716	−	3.30370i	0.147066	−	0.106849i
$957$	21.3616			0.690521
$958$	−28.7640	+	88.5266i	−0.929324	+	2.86016i
$959$	6.44464	+	4.68231i	0.208108	+	0.151200i
$960$	10.9401	+	33.6701i	0.353090	+	1.08670i
$961$	−1.09004	+	0.791960i	−0.0351626	+	0.0255471i
$962$	−5.43061	−	3.94557i	−0.175090	−	0.127210i
$963$	17.3092	+	12.5759i	0.557783	+	0.405253i
$964$	−36.3896	−	26.4386i	−1.17203	−	0.851530i
$965$	−34.8537	−	25.3227i	−1.12198	−	0.815167i
$966$	3.77521	−	2.74285i	0.121465	−	0.0882497i
$967$	−12.8545	−	39.5621i	−0.413373	−	1.27223i	−0.913698	−	0.406394i	$-0.866786\pi$
$967$	−12.8545	−	39.5621i	−0.413373	−	1.27223i	0.500324	−	0.865838i	$-0.333214\pi$
$968$	14.8107	+	10.7606i	0.476033	+	0.345858i
$969$	−15.3682	+	47.2985i	−0.493698	+	1.51945i
$970$	−7.15543			−0.229747
$971$	31.8709	−	23.1556i	1.02279	−	0.743097i	0.0559335	−	0.998434i	$-0.482187\pi$
$971$	31.8709	−	23.1556i	1.02279	−	0.743097i	0.966852	+	0.255337i	$0.0821865\pi$
$972$	−17.3765	+	53.4792i	−0.557350	+	1.71535i
$973$	0.761106	+	2.34244i	0.0243999	+	0.0750953i
$974$	17.7565	+	54.6488i	0.568954	+	1.75106i
$975$	−16.1267			−0.516469
$976$	−0.228309	−	0.702664i	−0.00730800	−	0.0224917i
$977$	−3.41138	−	2.47851i	−0.109140	−	0.0792947i	0.531877	−	0.846822i	$-0.321487\pi$
$977$	−3.41138	−	2.47851i	−0.109140	−	0.0792947i	−0.641016	+	0.767527i	$0.721487\pi$
$978$	−5.76264	+	4.18680i	−0.184269	+	0.133879i
$979$	8.99822	−	27.6937i	0.287584	−	0.885093i
$980$	3.17577	−	9.77402i	0.101446	−	0.312220i
$981$	−15.2040			−0.485425
$982$	4.86056	−	3.53140i	0.155107	−	0.112692i
$983$	−48.4149			−1.54420			−0.772098	−	0.635503i	$-0.780793\pi$
$983$	−48.4149			−1.54420			−0.772098	+	0.635503i	$0.780793\pi$
$984$	−20.5399	−	14.6860i	−0.654787	−	0.468174i
$985$	44.5462			1.41936
$986$	118.560	−	86.1389i	3.77572	−	2.74322i
$987$	−4.04090			−0.128623
$988$	32.5819	−	100.277i	1.03657	−	3.19023i
$989$	4.55000	−	14.0035i	0.144682	−	0.445284i
$990$	25.5548	−	18.5666i	0.812184	−	0.590086i
$991$	32.0350	+	23.2748i	1.01763	+	0.739348i	0.965795	−	0.259307i	$-0.0834943\pi$
$991$	32.0350	+	23.2748i	1.01763	+	0.739348i	0.0518310	+	0.998656i	$0.483494\pi$
$992$	6.22048	+	19.1447i	0.197500	+	0.607844i
$993$	34.8007			1.10437
$994$	−4.04040	−	12.4351i	−0.128154	−	0.394416i
$995$	−20.0517	−	61.7129i	−0.635683	−	1.95643i
$996$	−6.51310	+	20.0452i	−0.206375	+	0.635158i
$997$	−25.8753	+	18.7995i	−0.819478	+	0.595386i	−0.916563	−	0.399890i	$-0.869048\pi$
$997$	−25.8753	+	18.7995i	−0.819478	+	0.595386i	0.0970848	+	0.995276i	$0.469048\pi$
$998$	−49.8578			−1.57822
$999$	0.957653	−	2.94735i	0.0302988	−	0.0932502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.h.c.78.2	✓	40
41.10	even	5	inner	287.2.h.c.92.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.h.c.78.2	✓	40	1.1	even	1	trivial
287.2.h.c.92.2	yes	40	41.10	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91136 + 1.38868i) q^{2} -1.05524 q^{3} +(1.10682 - 3.40644i) q^{4} +(0.886655 - 2.72884i) q^{5} +(2.01694 - 1.46539i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.15479 + 3.55408i) q^{8} -1.88648 q^{9} +O(q^{10})\)	\(q+(-1.91136 + 1.38868i) q^{2} -1.05524 q^{3} +(1.10682 - 3.40644i) q^{4} +(0.886655 - 2.72884i) q^{5} +(2.01694 - 1.46539i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(1.15479 + 3.55408i) q^{8} -1.88648 q^{9} +(2.09479 + 6.44709i) q^{10} +(0.763287 + 2.34915i) q^{11} +(-1.16796 + 3.59460i) q^{12} +(-3.82457 + 2.77872i) q^{13} +2.36257 q^{14} +(-0.935630 + 2.87957i) q^{15} +(-1.34734 - 0.978898i) q^{16} +(2.33884 + 7.19820i) q^{17} +(3.60574 - 2.61972i) q^{18} +(-5.03769 - 3.66010i) q^{19} +(-8.31428 - 6.04068i) q^{20} +(0.853704 + 0.620252i) q^{21} +(-4.72115 - 3.43012i) q^{22} +(-1.51428 + 1.10019i) q^{23} +(-1.21858 - 3.75039i) q^{24} +(-2.61535 - 1.90016i) q^{25} +(3.45138 - 10.6223i) q^{26} +5.15639 q^{27} +(-2.89769 + 2.10530i) q^{28} +(-2.53256 + 7.79443i) q^{29} +(-2.21049 - 6.80320i) q^{30} +(-1.75753 - 5.40911i) q^{31} -3.53934 q^{32} +(-0.805447 - 2.47891i) q^{33} +(-14.4664 - 10.5104i) q^{34} +(-2.32129 + 1.68652i) q^{35} +(-2.08799 + 6.42617i) q^{36} +(0.185722 - 0.571593i) q^{37} +14.7116 q^{38} +(4.03583 - 2.93220i) q^{39} +10.7224 q^{40} +(5.15150 - 3.80290i) q^{41} -2.49307 q^{42} +(-6.36412 + 4.62380i) q^{43} +8.84708 q^{44} +(-1.67266 + 5.14790i) q^{45} +(1.36652 - 4.20572i) q^{46} +(-3.09804 + 2.25086i) q^{47} +(1.42176 + 1.03297i) q^{48} +(0.309017 + 0.951057i) q^{49} +7.63760 q^{50} +(-2.46802 - 7.59580i) q^{51} +(5.23242 + 16.1037i) q^{52} +(-3.56257 + 10.9645i) q^{53} +(-9.85571 + 7.16059i) q^{54} +7.08725 q^{55} +(1.15479 - 3.55408i) q^{56} +(5.31595 + 3.86227i) q^{57} +(-5.98336 - 18.4149i) q^{58} +(-0.126874 + 0.0921794i) q^{59} +(8.77352 + 6.37434i) q^{60} +(0.358906 + 0.260760i) q^{61} +(10.8708 + 7.89811i) q^{62} +(1.52619 + 1.10884i) q^{63} +(9.45962 - 6.87282i) q^{64} +(4.19160 + 12.9004i) q^{65} +(4.98193 + 3.61958i) q^{66} +(0.807457 - 2.48510i) q^{67} +27.1089 q^{68} +(1.59792 - 1.16096i) q^{69} +(2.09479 - 6.44709i) q^{70} +(-1.71017 - 5.26336i) q^{71} +(-2.17849 - 6.70469i) q^{72} -8.41769 q^{73} +(0.438781 + 1.35043i) q^{74} +(2.75981 + 2.00512i) q^{75} +(-18.0437 + 13.1095i) q^{76} +(0.763287 - 2.34915i) q^{77} +(-3.64202 + 11.2090i) q^{78} -14.4096 q^{79} +(-3.86588 + 2.80873i) q^{80} +0.218230 q^{81} +(-4.56535 + 14.4225i) q^{82} +5.57649 q^{83} +(3.05775 - 2.22158i) q^{84} +21.7165 q^{85} +(5.74312 - 17.6755i) q^{86} +(2.67245 - 8.22496i) q^{87} +(-7.46765 + 5.42557i) q^{88} +(-9.53732 - 6.92927i) q^{89} +(-3.95177 - 12.1623i) q^{90} +4.72743 q^{91} +(2.07169 + 6.37602i) q^{92} +(1.85460 + 5.70789i) q^{93} +(2.79574 - 8.60439i) q^{94} +(-14.4545 + 10.5018i) q^{95} +3.73484 q^{96} +(-0.326183 + 1.00389i) q^{97} +(-1.91136 - 1.38868i) q^{98} +(-1.43992 - 4.43163i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9	\( 40 q - 3 q^{2} - 3 q^{4} - 4 q^{5} - 19 q^{6} - 10 q^{7} + 16 q^{8} + 60 q^{9} + 5 q^{10} - 10 q^{11} - 12 q^{12} - 17 q^{13} + 2 q^{14} - 3 q^{15} - 23 q^{16} - 8 q^{17} - 2 q^{18} + 23 q^{19} - 13 q^{22} - q^{23} + 46 q^{24} - 34 q^{25} + 3 q^{26} - 18 q^{28} - 18 q^{29} - 19 q^{30} - 3 q^{31} - 26 q^{32} - 6 q^{33} - 44 q^{34} + q^{35} - 38 q^{36} - 5 q^{37} + 28 q^{38} + 17 q^{39} + 14 q^{40} - 11 q^{41} - 24 q^{42} + 13 q^{43} + 66 q^{44} + 43 q^{45} - 20 q^{46} - 27 q^{47} + 39 q^{48} - 10 q^{49} + 106 q^{50} - 18 q^{51} - 30 q^{52} - 30 q^{53} - 109 q^{54} + 118 q^{55} + 16 q^{56} - 40 q^{57} - 23 q^{58} - 37 q^{59} + 96 q^{60} - 41 q^{61} - 13 q^{62} - 30 q^{63} + 10 q^{64} + 6 q^{65} - 30 q^{66} - 6 q^{67} - 26 q^{68} - 31 q^{69} + 5 q^{70} - 31 q^{71} + 107 q^{72} - 46 q^{73} + 75 q^{74} - 61 q^{75} + 43 q^{76} - 10 q^{77} + 34 q^{78} + 76 q^{79} + 64 q^{80} + 16 q^{81} - 16 q^{82} - 52 q^{83} - 7 q^{84} + 86 q^{85} - 17 q^{86} - 20 q^{87} - 52 q^{88} - 16 q^{89} + 6 q^{90} + 18 q^{91} + 97 q^{92} + 32 q^{93} - 5 q^{94} - 102 q^{95} + 38 q^{96} - 18 q^{97} - 3 q^{98} - 71 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 - 3 * q^4 - 4 * q^5 - 19 * q^6 - 10 * q^7 + 16 * q^8 + 60 * q^9 + 5 * q^10 - 10 * q^11 - 12 * q^12 - 17 * q^13 + 2 * q^14 - 3 * q^15 - 23 * q^16 - 8 * q^17 - 2 * q^18 + 23 * q^19 - 13 * q^22 - q^23 + 46 * q^24 - 34 * q^25 + 3 * q^26 - 18 * q^28 - 18 * q^29 - 19 * q^30 - 3 * q^31 - 26 * q^32 - 6 * q^33 - 44 * q^34 + q^35 - 38 * q^36 - 5 * q^37 + 28 * q^38 + 17 * q^39 + 14 * q^40 - 11 * q^41 - 24 * q^42 + 13 * q^43 + 66 * q^44 + 43 * q^45 - 20 * q^46 - 27 * q^47 + 39 * q^48 - 10 * q^49 + 106 * q^50 - 18 * q^51 - 30 * q^52 - 30 * q^53 - 109 * q^54 + 118 * q^55 + 16 * q^56 - 40 * q^57 - 23 * q^58 - 37 * q^59 + 96 * q^60 - 41 * q^61 - 13 * q^62 - 30 * q^63 + 10 * q^64 + 6 * q^65 - 30 * q^66 - 6 * q^67 - 26 * q^68 - 31 * q^69 + 5 * q^70 - 31 * q^71 + 107 * q^72 - 46 * q^73 + 75 * q^74 - 61 * q^75 + 43 * q^76 - 10 * q^77 + 34 * q^78 + 76 * q^79 + 64 * q^80 + 16 * q^81 - 16 * q^82 - 52 * q^83 - 7 * q^84 + 86 * q^85 - 17 * q^86 - 20 * q^87 - 52 * q^88 - 16 * q^89 + 6 * q^90 + 18 * q^91 + 97 * q^92 + 32 * q^93 - 5 * q^94 - 102 * q^95 + 38 * q^96 - 18 * q^97 - 3 * q^98 - 71 * q^99

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